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