Time and Gravity

**Abbreviations used-**

Flexi-time or ∫(t) is used to convey the meaning that the passage of time is variable. Although it is constant within its own reference frame, from any other reference frame it can be variable. Flexi-time is used throughout this paper as a reminder that time is only constant within a limited reference frame, in general and from most reference frames it is flexible. (This is unlike light, which is a constant speed in a vacuum for all reference frames.)

**The problem with time and gravity**

Time, which in itself is a difficult subject, is made more difficult because we cannot ‘look’ at it from the outside, nor can we divorce ourselves from it in any way. This is very much like the problems we have in understanding gravity. The problem is compounded by having a limited language that frequently leads to what appears to be contradictions.

Everything in the universe is made of energy but energy; on its own does not a universe make.

The universe is made of two things, energy and matter. Time is an expression of that relationship. The universe has to contain both energy and mass (gravity) for the concept of either time or universe to have any real meaning.

E = mc2

c2= E/m

c = √E/m

c = d/ t

d/t= √E/m

c2 = E/m

Where E = energy, m = mass, c = speed of light, d = distance, t = time

We can see from this that as m goes toward 0

E goes towards ∞

Then the speed of light goes toward ∞

We can also see that as if m = ∞ it can only do this if E = 0

In which case

The speed of light is 0

We can see from the above that looked at in this way the speed of light can vary between 0 and ∞.

d/t= √E/m

d = √E/m x t

d = ∞

We can see that **in a hypothetical universe that contains energy but no matter** the

‘Speed’ of light and distance are both infinite. If you have an infinite rate of flow of time then the speed of light would be infinite. However, without gravity there is no arrow of time, so the concept of time becomes meaningless, hence the speed of light, in that scenario is meaningless. What we can say is that light ‘travels’ instantly and without causality in all possible directions and to infinite distance, although in this scenario, the concept of distance is also meaningless.

Likewise **in a hypothetical universe that contains only matter and no energy** the speed of light is 0. Therefore, time does not exist.

d/t= √E/m

d = √E/m x t

d = ∞

Distance is zero.

How can you have a universe in which time does not exist? If we think of a hypothetical universe containing only mass, the mass is contained within a singularity. It contains zero space-time. If we introduce energy then it must be contained within the Schwarzschild radius, as there is ‘nothing’ outside. By increasing the energy level, the Schwarzschild radius increases. The universe is by definition contained within a Schwarzschild radius.

Matter plus energy = space and time.

It contains an arrow of time but the clock never ticks. Matter is the only thing in this universe (and its associated gravity) so the arrow of time must be a product of matter/ gravity.

We can see that in a **hypothetical universe that contains energy but no matter** the

‘speed’ of light is infinite. Theoretically, if you have an infinite rate of flow of time then the speed of light would be infinite. However, without gravity there is no arrow of time, so the concept of time becomes meaningless, hence the speed of light, in that scenario is also meaningless. What we can say is that light ‘travels’ instantly and without causality in all possible directions and distances. *Another way of seeing this scenario is to say the speed of light is ***infinite in both directions as the arrow of time is equally double ended.** I will use this term in the remainder of this paper as by retaining ‘time’, it allows things to happen within ‘time’ even if there is no causality.

From the above we can see that although the speed of light is infinite it has no direction.. In which case it must flow in all possible directions. Keeping it as simple as possible let us assume that the arrow of time has just two directions, forward and backward. We know the arrow points forward but if antimatter is ordinary matter with a reversed arrow of time then the arrow of time is double ended. In which case m in any of the above terms can be replaced with m + -ma where ma is antimatter.

From the above we can see that it is the interplay of energy and mass that we call time.

Or more correctly ‘flexi-time’ henceforth referred to as ∫(t). Energy, what does it do, it wants to dissipate over the largest possible volume of space in the shortest possible time. This process is entropy.

We have also seen that mass wants to ‘slow photons down’. (Now we are getting into the language problem) What we can see, so far is the interplay of energy and mass are what we call flexi-time or ∫(t). The rate of flow of time in the universe is its energy divided by its mass. Mass curves space time and this space-time curvature is called gravity. Therefore, we could say that the flexi-time in the universe is equal to the square root of its energy divided by its gravity.

c = t√E/m

As speed is distance divided by time then distance and time are both relative terms.

d/t= √E/m

d = t√E/m

We can see that as m goes toward 0. E goes toward ∞

So d goes toward ∞

and

t = d/√E/m

If d = ∞ and E/m is infinity then √E/m is still infinity, so one could think that ∞/∞ = 1 but that would be wrong in this case as √∞ must be smaller than ∞ and ∞/ any number is ∞.

We can see that in a hypothetical universe that contains energy but no matter flexi-time is infinite (in both directions) as is distance.

Let us look at the opposite situation where mass is infinite and energy = 0.

d = t√E/m

We can see that as m goes toward ∞ then E goes towards 0

And

d = t√E/m

E/ ∞ = 0

d = 0 We can see that in a hypothetical universe that contains matter but no energy the rate of flow of time is 0 as is distance.

Therefore this universe must be contained within a single black hole singularity.

When Einstein wrote E = mc2 he was explaining how mass and energy are related through the speed of light. The energy mass equivalence formula was possibly not meant to explain some of what I have used it for here. However, I am only considering the same things as Einstein considered, the relationships between energy, mass, the speed of light, time and distance. Therefore, I believe E = mc2 is a valid tool to examine and predict certain characteristics of the universe. As you have just seen, it explains what ‘time’is.

**You may be confused by the use of the term flexi-time or ∫(t), if so a reminder. Flexi-time or ∫(t) is used to convey the meaning that the passage of time is variable. Although it is constant within its own reference frame, from any other reference frame it can be variable. (This is unlike light, which is a constant speed in a vacuum for all reference frames.)**

I have also considered the speed of light to be 0 and ∞ which quite obviously it cannot be, this was by way of math’s to see what was predicted. Einstein made it quite clear that the speed of light is invariant to all observers in any reference frame. He did not add “within the universe”. He presumably thought he did not have to. Sometimes, taking a hypothetical look at the universe from an outside reference frame clarifies what’s going on inside. Einstein was trying to make sense of the universe and he did a superb job of showing the mass energy equivalence principle bound together with the postulate that the speed of light in a vacuum is constant. This constant, the speed of light is the single most fundamental constant; it is upon this that all constants of nature depend.

For the speed of light to be a constant, there is only one-way, this can happen; light has to be the universal clock, the heartbeat of the universe. We measure this heartbeat as speed. Speed being distance, divided by time. Theoretically, the universe could have distance and time as standards but it does not for this reason. We know from Relativity that clocks vary in speed and measuring rods change their length. For the speed of light to be a constant flexi-time has to be variable. Speed is distance divided by time, so by having a variable flexi-time distance (length of a meter) is a standard.

From the above we have seen that the energy mass ratio in the universe is what defines the passage of flexi-time in the universe. Although is obvious that the ‘total energy’ (mass energy E = mc2 ) of the universe must remain constant. (The first law of thermodynamics) The mass energy ratio is continually changing in accordance with

E = mc2. Stars convert mass into energy for example.

∫(t) =c = d/t = √E/m

As ∫(t) = √E/m =c then for c to remain a constant ∫(t) has to be a variable.

As c = d/t then distance has to be a constant.

Another way of looking at this are, the speed of light and distance are a constant because the rate of flow of time is a variable.

This was shown to be the case by Einstein when he showed that clocks run slower [∫(t) is slower] in a gravity well.

This is shown by ∫(t) = √E/m. As gravity increases (due to an increase in mass) so ∫(t) decreases.

Flexi-time is real, not abstract, it is the energy of the universe divided by its mass. The universe can be considered a very large clock.

*End of part 1. See Theory of Time 2 of 2*