Universal Time

[Little Bang]

A clock just outside the event horizon of a black hole will appear to be almost stopped to an observer far away. That same clock will appear to run faster on Earth, faster on the moon and faster in empty space. Those four locations will have an average rate which suggests the Universe has an average rate based on the matter energy density of the Universe. In space I have a device that will emit a beam of light which I call device A. Three hundred thousand kilometers away I have a detector which I call device B. Some distance away I have a clock which is entangled with device A and B such that when A emits the beam my clock starts and when device B detects the beam my clock stops. I trigger device A to fire and my clock shows a time of one second determining the speed of light to have it's current value. I now move my clock to the edge of the event horizon of a black hole and trigger device A again. If my logic is correct don't I measure c to be almost infinite?

[Little Bang]

Assuming the above to be correct then if we run the Universe backwards to just after the BB when the mass/energy density is very high then the speed of expansion would be very high thus explaining inflation? Wouldn't this also suggest the Universe is much younger than we think?

[CraigD]

In space I have a device that will emit a beam of light which I call device A. Three hundred thousand kilometers away I have a detector which I call device B. Some distance away I have a clock which is entangled with device A and B such that when A emits the beam my clock starts and when device B detects the beam my clock stops. I trigger device A to fire and my clock shows a time of one second determining the speed of light to have it's current value. I now move my clock to the edge of the event horizon of a black hole and trigger device A again. If my logic is correct don't I measure c to be almost infinite?

Yes.

 

I think you should be careful about saying the light emitters and detectors are “entangled” with the clock, because this suggest signaling via quantum entanglement – an ansible – which current theory predicts is impossible. It’s not important to the thought experiment, though, as having the clock be the same distance from A as from B, and started and stopped by a radio or light signal from each device, will assure that the duration it measures is the same as if ansibles were used.

 

A clock just outside the event horizon of a black hole will appear to be almost stopped to an observer far away. That same clock will appear to run faster on Earth, faster on the moon and faster in empty space. Those four locations will have an average rate which suggests the Universe has an average rate based on the matter energy density of the Universe.

We can define an “average gravitational time dilation” for any volume of, or the whole, universe relative to a given inertial frame, by, say, dividing that volume with an equally spaced 3D lattice, and averaging the [math]\frac{t_{\mbox{slow}}}{t_{\mbox{fast}}}[/math] time dilation factors of all the lattice vertexes that lie outside of black hole event horizons.

 

[math]\frac{t_{\mbox{slow}}}{t_{\mbox{fast}}} = \sqrt{1-\frac{r_0}{r}} [/math], where [math]r_0[/math] is a black hole’s Schwarzschild (event horizon) radius. Relative to the distance between black holes, even for supermassive ones, [math]r_0[/math] is very small. Therefore because only a few vertexes are near enough event horizons to have time dilation factors much less than 1, the average time dilation factor of the universe or any large volume of it is not much different than the time dilation factor of a randomly selected vertex or one near a body much larger than its Schwarzschild radius, such as Earth.

 

Assuming the above to be correct then if we run the Universe backwards to just after the BB when the mass/energy density is very high then the speed of expansion would be very high thus explaining inflation? Wouldn't this also suggest the Universe is much younger than we think?

No.

 

The age of the universe may be assumed to be measured by a fast-ticking clock far from any large mass. Were we to compare this hypothetical clock to another close to the event horizon of the very young, pre-inflation big bang universe, the difference in time now, about 13,750,000,000 years later, the difference between them would be very small, because the inflationary period ended very shortly (less than 10^-32 seconds) after the big bang, so even if the slow-ticking clocks time dilation factor was nearly 0, the difference between the clocks due to that brief period of great time dilation would be less than 10^-32 seconds.

[Little Bang]

As to the first question. When the Universe had a diameter on the order of a million light years the mass/energy density would be very high, therefor the rate of a clock then would be much slower as compared to a clock today which also answers the second. It's disappointing that our knowledge sometimes can preclude the use of logic.

[CraigD]

As to the first question. When the Universe had a diameter on the order of a million light years the mass/energy density would be very high, therefor the rate of a clock then would be much slower as compared to a clock today which also answers the second.

You seem to have misunderstood my post, the theory of general relativity’s gravitational time dilation formula, and the sequence and duration of events described by the big bang theory.

 

The gravitational time dilation formula is: [math]\frac{t_{\mbox{slow}}}{t_{\mbox{fast}}} = \sqrt{1-\frac{r_0}{r}} [/math],

 

where [math]r_0 = \frac{2Gm}{c^2}[/math], [math]r[/math] the distance of the point from the center of mass of a body of mass [math]m[/math], [math]G[/math] is the constant of gravity, and [math]c[/math] is the speed of light.

 

The important thing to notice about this formula is that mass/energy density is not a variable in it. It has only 2 variables: mass [math]m[/math] and distance [math]r[/math]. Although the average density of a sphere of radius [math]r[/math] and mass [math]m[/math] is also defined by these 2 variables, this formula,

 

[math]\rho = \frac43 \pi m r^3[/math],

 

is not proportional to the gravitation time dilation formula.

 

This is a critical distinction, LB. Your assumption that gravitational time dilation – as you state it “the rate of a clock then (in a volume with high average density) would be much slower as compared to a clock today (in a volume with lower average density)” – is simply incorrect and false.

 

You may have gotten this false impression from observing, correctly, that the average density of the volume enclosed by a star mass black hole is very high, on the order of 10¹⁸ kg/m³. This is not true, however, for much larger black holes. For example, the supermassive black hole in the center of the Andromeda Galaxy has an average density on the order 1000 kg/m³, about the same as water.

 

The gravitational time dilation experienced at a point [math]r = \frac{2Gm}{c^2} k[/math] (where k is any constant greater than 1) from the center of any body of any mass [math]m[/math] is the same, is the same, regardless of the average density, or any other density measurement, of the body or radius [math]r[/math] sphere surrounding it.

 

For gravitational time dilation, density doesn’t matter – only mass and distance.

 

None of this negates questioning if gravitational time dilation due to the large-scale timeline of the big bang might have significantly affected the subjective time experienced by a significant number of particles of processes since the big bang. If this happened, it would have significant consequences - for example, some or most primordial elements would be much younger than others. However for it to have happened conditions in which significant volumes of space were subject to significant time dilation for long periods of time are necessary.

 

According to big bang theory, the whole universe was once very small – so , presumably, might have had such volumes of space. However, it was not very small for a long period of time – much, much less than 1 second.

 

This very brief duration is the real killer for your idea, LB. No matter how great the gravitational time dilation in the early universe – how much slower its clocks ticked – the duration of this period was much too short to have had a significant affect on the age of anything.

 

It's disappointing that our knowledge sometimes can preclude the use of logic.

Are you accusing me of just reciting “canned” knowledge, without logic? :angry:

 

I don’t think this is a fair description. I can’t recall having encountered your specific question before, so am not just “reciting” it, and had to use logic to apply general theory to answer it.

[Little Bang]

I am as guilty as anyone else of allowing information contained in my memories to dictate a response to a query without fully appreciating the magnitude of the problem. The density of Andromeda's BH is based on the volume of space contained within the event horizon, a place no one knows anything about. That said I can speculate the energy density at it's center is almost infinite. Allen Guth's inflation theory is supported by some because it solves some problems but there are also some who think it is not correct. I will finish with this, where there is matter the energy density is high. Where there is no matter the energy density is low. Clocks run fast where the energy density is low and high where it is high. In the early Universe it is obviously high as compared to now.