2. Expansion of the Universe as Travel in Time Direction

Below post is a back-up of my posts in my Quora blog. I take a copy of them to here in case if something goes wrong in there.

(If you somehow have ended up on this page without any background knowledge, before continue, you better check the first post of: 1. Do We Travel in Time Direction With Speed Of Light?, if you are willing to understand this concept)

Most of you have probably heard that our Universe is expanding. This causes galaxies to getting far away from each other every moment (doesn’t work inside the galaxies since the gravity is dominant there). You may have also heard that after enough distance (about 14 billion light years) the objects will move away from each so fast that, their separation speed will be greater than the light’s. Yes, according to relativity theory, nothing can move faster than light but apparently space itself doesn’t have to obey that. In our case of expansion of the universe, what expands is the space itself and objects are actually not moving. All they do is to drift together with the space while it is expanding, just like being drifted on a river inside your raft while not moving anywhere on your own.

This has some interesting consequences. After enough distance (about 93 billion light years) it is not possible for the light to reach from one object to the other due to expansion of the universe, providing us a limit for the Observable universe. Pretty amazing, right? We are limited to observe the universe up to a certain distance just like a scuba diver has a limited sight under the water. Once the diver start to swim towards a direction, his vision will be expanded into that direction just like what exactly happens about the observable universe.

Expansion of the universe is also considered as one of the biggest proofs for the Big BangTheory. The theory which explains the existence of our universe starting from a singularity into the universe that we know today via an expansion just like an explosion. One strange thing about Bing Bang though, when you ask where is the center of this explosion, the answer you get is; everywhere.

This concept has been puzzling me since long time. I was trying to understand, how can something expand when the center is everywhere? As you can also understand from the balloon example, we should again think in higher dimensions. Since surface of the balloon is a 2 dimensional geometry and the center of the expanding balloon can only be found leaving this 2 dimensional geometry and by travelling in 3 dimensions till its center, that means we also should travel in 4D direction to reach to the center of this Bing Bang of our universe. And since it is not possible for the humble 3D creatures like us to imagine 4D, we again should go down to safer lower dimension environments and create some theoretical universes as I have explained in my 1st post since it is possible for us to examine them.

Let’s start to create our 1 dimensional expanding universe model. Everything should be similar to ours except all are in lower dimensions. So, now we have a big bang which has happened in 1 higher dimensional environment (2D). We will mention the radius of this explosion with R, Our objects should have their own observable universe limit which we know is equal to 93 billion light years (as co moving distance, never mind it is complicated). It is located between -x and +x on the blue line. I will draw few objects in that universe which I call “A”, “B” and “C” to observe their movement during the expansion. Please note that the distances between the objects are not scaled and is not big enough to affect the observable universe limit. So our 1D universe which expands in 2D environment should look something like that:

As you are familiar from the 1st post, these objects are only familiar with their own 1D universe which consists of the blue line and they neither see they are located on a bigger black arc universe nor they are a part of the explosion on a 2D environment since they are only 1D objects in their own observable universe. The curvature on the blue line is indicated for visual purpose only. On a vast universe with a huge R, this curvature will not be noticed and will behave like a straight line rather than an arc.

I would like to try and see what happens to our objects in such an expanding universe. But before that, there is a critical decision that we should make. What will happen to the length of the blue arc (observable universe length) during the expansion? Will it decrease, extend, or stay the same? For that, we should look into the definition of the observable universe limit first. It is defined by the expansion rate and speed of light. We know that speed of light is invariant. But the expansion rate of the universe has been recently found as increasing. Therefore, we can say that the size of the blue line can also increase together with the expansion. But why should it increase proportionally? Let’s think about the beginning of the expansion where the R was very small. If blue line always tends to stay as it is, at the beginning, where everything was very close to each other on that small R circle, the length of the observable universe could be bigger than the whole universe before a certain point. Therefore, I assume that the observable universe proportionally increase in length together with the expansion of the universe.

Now we can try to see what happens to these objects when their own 1D arc universe expands into 2D environment after a certain amount of time passes.

Here, time has passed as t’-t amount. The universe has expanded from R radius to R’. Observable universe has expanded from +x, -x to +x’, -x’ while the distance between A and B has increased from L to L’.

Let’s assume that A and B were located 3,26 million light years (ly) or 1 mega parsec (mp) apart from each other before we have spent our time. We know that the expansion rate in our universe is about 70 Km/sec per mp. We also know that the length of our observable universe (+x - (-x)) is about 93 billion ly. Let’s assume that the time spent (t’-t) is 1 second. One parameter which we have missing is the speed shown with red arrows. The expansion rate of 70 km/sec per mp gives us how fast the objects separate from each other on the blue line. But we need the speed rate on the red arrows direction. And I have a very good reason to believe that this speed is equal to the speed of light from my 1st post. If you have carefully read that post, you will see that all the criteria defined in the 1st post about our travel on time direction matches with our red lines above. So we also know our speed in red arrows direction. It is speed of light. Therefore, R’ should be equal to R+300.000km after 1 seconds.

From the above geometry, we can get 2 triangles to play with. “O” is the center point of the Big bang which wasn’t shown before. I will ignore the curvature of our lines between the objects considering R as a huge number making our arc almost straight.

From these 2 we can calculate:

|A’B’| / |AB|=|OB’| / |OB|

(|AB| + 70) / |AB| = (|OB| + 300.000) / |OB|

1 + 70 / |AB| = 1 + 300.000 / R

R= 300.000 x |AB| / 70

R = 300.000 x (3.260.000 x 9,469 x 10^12) / 70

70R= ~ 9,2532 x 10^24

R= ~ 1,322 x 10^23km

R= ~ 13,96 x 10^9 ly

Isn’t this amazing? This is considerably close (with about %1 deviation) to the known age of our universe which is about 13,8 billion years. But wait a minute. If we know our distance to Big bang, we can also calculate the circumference of our universe, right? Let’s do it.

C=2πR=2 x π x 13,96 x 10^9 =~ 87,7 x 10^9 ly.

That’s a bit strange. The circumference of the whole universe seems to be almost equal to the diameter of the observable universe that we know today. Meaning, our blue curve is almost equal to our black circle. Anyway, I will skip that issue for now.

So, our universe has started to expand about 14 billion years ago. That amount is equal to 14 billion ly when you assume that you travel in time direction with the speed of light. So that represents the radius of the universe. We can only look back in time to see the center if it is in time direction. But hey, isn’t it what we do when we look at the distant stars? The further we look, the older phase of the universe we see, right? So, if looking further means looking back in time, when we look at the furthest, we should be able to see the center of the Big bang, in every direction, right?

In order to understand this idea better, let’s raise our dimension environment 1 level and go to a 2D environment as below.

In this 2D universe model, present time is the curved surface shown with the green arrows and the circle. It exists along x and y axis giving its 2D nature. And the previous phases of the expansion have been shown with smaller circles in time direction which is identified as t. It goes all the way down to the Big bang which is shown as a red dot. The radius of the universe which is shown with R increases as the time passes since the Big Bang. If you cannot see the circle which R belongs to, wait for it.

(Out of the subject note: Did you notice how does the perpendicular time direction introduces us a 3D environment over that 2D universe? It was same in 1D universe example and t axis was introducing us a 2D environment together with x axis over that 1D universe. In my next post, I will try to explain this idea about how to construct higher dimension environments together with the motion in time direction with speed of light. But let’s continue to our topic now.)

The above graph is only a small part of the picture and tells us the story partially in my opinion. Just like our universe was curved in our 1D example. This observable 2D universe (which is a surface instead of a line), should also be curved and should belong to a part of the bigger universe, just like the below one.

Now, we can see a balloon like 3D environment which our 2D observable universe expands together with it. The top part of the balloon where it intersects with our current time circle creates a curved 2D surface as our observable universe. Something like this:

Notice that this is just a surface. It is a curved one but it is still a 2D shape. That curvature, which only is possible on a 3D environment, won’t exist for the objects of such a 2D surface universe. If there were intelligent creatures on such a universe, they could understand that curvature by looking at the further objects and see how they lose sight on them after a certain distance just like we do at the earth’s horizon. That distance would depend on the R of their universe. Bigger the curvature, shorter the distance to lose sight on the horizon.

But this is also not the real picture of our universe. We know that our universe has 3 spatial dimensions and cannot be represented by this 2D curved space. But if we are convinced that this is a good way to describe it, we can use this 2D shape as an analogue to describe our universe in 3D.

Above described observable universe is a 2 dimensional surface and expands on a 3 dimensional volume. So, similarly our universe should also be a 3 dimensional object, probably curved like a sphere or a spheroid which expands into a 4 dimensional entity. Since the above 2D observable universe is a curved surface, we can also assume that ours is a sphere which is curved into a 4D entity. Notice that in above example, universe continues to outside of our observable one and it resembles our 3D balloon universe. Similarly, our curved 3D observable universe also continues beyond its border and resembles a 4D hyper sphere as the whole universe. And this big picture can even be a small part of a higher dimensional universe but I won’t go into that now.

The diameter D of the observable universe is not exactly defined above. It can be equal to the diameter of the whole universe making observable universe the whole or half of the sphere or it can also be a very tiny part of what I have drawn above. I have reasons to think any of these probabilities but I will postpone dealing with that to future.

And this is basically how an expanding universe can be pictured. But, what is so fascinating about that idea? With the above model, you can understand that the answer to the “where did the big bang has happened” doesn’t have to be “everywhere” anymore. It is possible to understand where the explosion point is and how can it be not possible to see it around us, as well. Our observable universe can possibly be a curved 3D sphere which is a bigger 4D hyper sphere and the explosion point can be located within that 4D environment, or maybe even in a higher one?

Above picture is only valid in a universe with a constant speed expansion. But it has been found out that it has an accelerating nature. This tells me that our universe even has a higher dimensional structure. Therefore, my next post hopefully will be about the motion based connection between the dimensions. I will try to explain how each time derivative (or integral) of motion introduces us a new level of dimension.

And if you have something to say about any of the above, you are very welcome to the comments section for the discussion.

P.S.1 If you have a look at Hubble's law page, you will see that expansion rate of the universe has been measured with different rates varying between 67 to 80 km/sec. since 1958. However, the age of the universe is a more solid number (13.799±0.021 billion years). So, we can do our above calculation again, this time accepting age of the universe as a known fact but expansion rate as our target and we can reach to a more precise expansion rate if the above theory is true.

|A’B’| / |AB| = |OB’| / |OB|

(|AB| + X) / |AB| = (R + 300.000) / R

X=70,818582 km/sec

If one day, it will be measured precisely and will be found as equal to this value, then we can claim that we already knew the exact value for the expansion of universe by this calculation.

P.S.2 According to this theory, the real expansion speed of the universe is equal to speed of light and what they today call as expansion rate of the universe is more like a stretching rate of the universe. But not to have a confusion, I will keep calling it as it is widely accepted today and real expansion of the universe as our travel on time direction.

1,567 views · 4 upvotes · Written Jun 17

1. Do We Travel in Time Direction With Speed Of Light?

Below post is a back-up of my posts in Quora blog. I take a copy of them to here in case if something goes wrong in there.

(First of all, I must say that this is not my own idea and it has been widely discussed before, including many topics in Quora. After my answer about “How does Electromagnetic wave emit photons” I have thought a lot about this and saw that it is possible to validate the idea by taking the speed of light (c) as the universal speed limit as described in Relativity Theory. It also has some useful ideas to understand the Time dilation effect, so I wanted to share my thoughts on this.)

There is one important question to reply before we start the subject. Isn’t it obvious that we don’t move with c to any direction? If we happen to move with c at time direction, we would notice it, won’t we? Everything around us seems to stand still or move with comparatively slow speed rates. So, why there is need for such a question even? Isn’t the answer obvious; No, we don’t travel in time direction with speed of light? Well, unfortunately these arguments are easy to falsify;

1. As far as we know, there is no such thing as absolute rest in universe. Everything in universe moves compare to another object and there is no way to tell which one is the reference point. Moon rotates around the earth, earth around the sun, sun around the galaxy center, galaxy around the galaxy cluster etc. So, there actually is no reference point to determine who moves and who stays still. If so, then we can also assume that, maybe everything (I mean everything) around us also moves at same direction with the same speed. If this is the case, how can you notice it? There is no reference point around us to tell if you move or not. Have you ever sit inside of your car while it is being washed in an automatic car washing machine? Did you ever have the feeling that your car moves when the cleaning rolls pass over you? Was your car really moving or was it just the impression which the rollers movement gave you? If you didn’t know the car doesn’t move at the first place, let’s say if you woke up at the middle of washing process, could you tell you or the rollers move? Well, what if the same phenomena is valid for our entire universe? We all can be moving at the time direction and thinking that we stand still by looking at the objects around us which actually also move together with us.

2. Maybe we notice it, as flow of time. There is a big struggle to explain what actually is the flow of time and there is no certain theory yet.

So, if we really move in direction of time with so high speed, which direction does it move towards? Before we go into that, we need some background knowledge. Einstein has taught us with Relativity Theory (RT) that there is a connection between time and space. And speed is one of the tools which lets us to see this connection (also is gravity, but we won’t use it, for now). According to RT, time slows down (relatively, meaning compare to other objects) whenever an object speeds up and this is called time dilation effect. So, if we are really travelling in time direction with c, then it might also be possible that with our own movement, we somehow affect the movement (flow) of time, let’s say, we may steal some of its speed, so it slows down. But in order to do that, we should either move at the opposite direction of time or there should be another sort of mechanism causing time to slow down while we are speeding up.

So determining which direction time travels to, is even more important now. And since we have a tool (our own speed) to slow down the time, maybe we can use it to determine its direction, as well.

We know that the time dilation effect is independent from our travelling direction. Wherever we move to, time slows down. Time dilation seems to care about our speed rate, only. Now let’s analyze this situation; if we could be able to travel at the opposite direction of time, time should slow down towards one direction only and we could say that time travels to the opposite of this side. But there is no such direction that slows down time. All directions seem to be equally responsible from its flow as time dilation shows us. So we must find a direction which is equally opposite to (or distant from, whatever that means) each and every direction that we know of. How can this be possible?

So at this point, it is obvious that the answer will not be ordinary. We need our imagination in order to reply this question because the reality we live in doesn’t let us to reach the answer, there absolutely is no such direction in our universe. Or, there is one more possibility; there is no such dimension in the universe that we are familiar with. Since the directions are all about the dimensions, it is also another possibility that time travels in another dimension which we are not able to perceive.

As far as we know, we live in a universe which has 3 spatial dimensions + 1 temporal dimension which is called time and all of them are called together as Space-Time (ST). What we know from our 3 spatial dimensions is that all of them take place with an angle which is perpendicular to each other, the usual x, y, z axes. If we will assume that time moves with a physical speed of c, then we should assume that it is moving in another spatial dimension instead of the temporal one. We have just understood in the last paragraph that time cannot be travelling in any of our 3 usual spatial dimensions, so we must find out a 4th one. We also know that it should be perpendicular to the existing 3 spatial dimensions. One possible solution which fits into these criteria is to imagine the 4th spatial dimension as a sphere which intersects with all our 3 spatial dimensions with 90° but this brings a lot of problems for our imagination. Our brains are simply not wired to think within a 4 dimensional environment since they never needed to do so (I willingly didn’t say; “since they don’t live in it” and we will come to that in future).

One common practice to apply in such cases is (at least what I do is) to create scenarios in lower dimensional Space-Times. Since we are able to image 3 spatial dimensions, if we create a hypothetical 1 or 2 dimensional Space-Time, we will still have enough directions left to play with. So we can use them to imagine the directions that we are not capable of imagining in our universe, like the extra dimension that we need for time to move towards.

In order to do that, let’s create that hypothetical lower dimensional space-time environment. To keep things simple, let’s do it 1 dimensional. So, in this 1D space-time environment we have an object which we will call as “A”. Length of it is irrelative for us. This object is only able to move along 1 line which doesn’t have any thickness and depth. We will call this line as “x” axis. For our object A, the universe is only consists of this 1D line so it is only able to move in its direction towards +x or -x. So this universe will look something like that:

“A” does not only move along x axis, it doesn’t even know that anything outside of “x” exists. It cannot perceive anything beyond it. But we can, and we will use this knowledge to our advantage to solve our mystery. Now, we have an extra dimension which we can place the A’s movement in time direction according to our previous criteria. According to this criteria, ttime direction should be perpendicular to x and we can easily do it in this 1D space-time environment as below.

Now, we have marked a new axis which we call as “t”. It represents the time direction which we assume that we are moving with c towards it. Length of c represents the speed rate of light so its legth is important for us. Our poor object “A” doesn’t even know whats going on since it has no ability to understand such a direction can exist.

We have finished to set up our scenario in a lower dimensional space-time and now we can observe what happens to speed of time when A moves in “x” axis. It is obvious that “A” doesn’t move at the opposite direction of time, it moves on its own “x” axis which is perpendicular to time’s direction. So what can be the mechanism to slow down A’s movement in “t” direction when it starts to move in “x” direction? There is such a mechanism which was also introduced by RT; speed of light as the universal speed limit. Again, according to Einstein, speed of light cannot be exceeded in our universe. And it is always same for all observers and for all reference frames independent from their speed and location. That means wherever we go, doesn’t matter with which speed, we will always measure speed of light with the same speed and we can never exceed it. We will use this knowledge as our mechanism. Now let’s assume that “A” moves towards “+x” direction with V1 speed rate as below:

In this case, as soon as A starts to move, It will not be only moving in time direction anymore but will also move in “+x” direction, thus creating a combined speed for “A”. One of the components of this combined speed will be V1 and the other one must be its speed in time direction which was “c” as shown with fainted red arrow. According to this, the combined speed rate of “A” should be equal to the length of the black arrow between the starting point “O” and “t1”. But there is a conflict now. RT says that nothing can move with a speed rate greater than c and speed of A seems higher than c according to our graph. We should find a solution to this conflict. We definitely know that A is moving with V1, since A sees its own speed so it is confirmed. We also know that c is the highest possible speed in our universe. The only component in this picture which we aren’t sure is our speed in time direction. So the only possibility is that our speed in time direction should be decreasing to keep our combined speed as c when we move in “x” axis.

This will give us a new look. Now our combined speed is C, shown with red arrow above. Speed rate of “A” on “+x” direction stays the same as V1 but now our speed in vertical “t” axis has been decreased from c to “U1” which is shown with dark red arrow. You can also see the difference between c and U1 as “t1-t2” in above graphics. Now let’s increase “A”s spees in “+x” direction and see what happens.

Now “A” moves towards “+x” with a greater V2 speed. Now it is easier to see that the combined speed of “A” always stays as c and this creates an arc with a radius of c. The vertical component of “A”s combined speed is even smaller now (U2). And its speed in time direction is a lot slower (t1-t2 is greater than the previous graph).

This shows us that when “A” moves in any “x” direction (which is the only axis it is able to move in his own 1D space-time), its speed in time direction starts to get slower. And if it increase its speed on “x” axis, it starts to move in time direction even slower. This is in-line with the definition of time dilation; time flows slower, when you increase your speed. But if what we have concluded above is the same thing as time dilation, their rates should also exactly match, right? Let’s try to calculate the amount of time dilation from our simple geometry and see.

This is the time dilation formula from its source :

In this formula; ∆t’ is the time spent while in rest and ∆t is the time spent when in motion.

Now let’s try to calculate the same thing from our graph. The time was travelling with c when “A” was not moving and we have assumed that it represents the flow of time. So we can assume that c is the amount of time that “A” spent when it was in rest. It is also visible that it is equal to t1 of our graph.

c=t1

The time travels with U amount when “A” was in motion according to our graph and it isalso equal to t2.

U=t2

From these 2 equation, we can easily reach to:

There is one more useful equation that we can create according to our graph with the famousPythagorean Theorem. Our triangle is the below one:

And our formula for this triangle would be:

$c²=U²+V²$ (ignoring indexes of U and V, calculating it for all cases)

If we rearrange the formula for U:

$U²=c²-V²,$then we reach to:

Now let’s go back to our previous equation:

If we replace U with our previous finding:

Let’s keep the dilated time (t2) at one side of the equation:

And some rearrangement:

So, we finally reach to:

Let’s compare this one with the original time dilation formula below:

Yes, almost exactly the same. Except, our formula is the inverse version of the original one. And why is that? Actually it makes sense when you think about it.

The original time dilation formula gives the time dilation between the objects which is in rest with 0 speed rate and objects which move with v.

The time dilation formula that we reach to, gives the time dilation between the objects which in rest with c speed rate and objects which move with v.

When you set the speed of an object at rest from 0 to c, everything becomes up-down. You no longer speed up when you move with V but you slow down in time axis. Therefore, t2, dilated time becomes smaller.

Now let’s give a value to V and see what happens with both formula: We will take v as 0,5c for simplicity.

With the original time dilation formula:

∆t’=∆t/(1–(0,5c)²/c²)^(1/2)

∆t’=1,1547 ∆t

With our formula:

t2=t1 (1–(0,5c)²/c²)^(1/2)

t2= 0,86 t1

Of course, only one of these results is correct and it is the one calculated with the original time dilation formula. But what does my result tells us? I interpret it as; we really move in time direction with speed of light. That much of similarity between 2 calculations is beyond being a coincidince. But reaching to an inverse time dilation formula tells me that; when we speed up in our own space-time environment, we really slow down in time direction. But this slowing down affects the flow of time inversely. The slower we move in time direction, faster our time flows relative to the objects which move in our space-time environment with slower speed rates.

Well, that concludes my topic; we do travel in time direction with speed of light depending on our speed in our own environment. But as usual, it brings more questions with this reply. Why does the time flows faster when our speed in its direction slows down? What kind of mechanism takes part in that process? Hopefully I can find a meaningful answer and write another blog post about it. Will inform you if I can.

And if you have something to say about any of the above, you are very welcome to the comments section for the discussion.

320 views · 3 upvotes · Written Jun 4