# A Theory for Science-Fiction Time-Travel

From H.G. Wells onward, there have been many stories concerning the phenomenon of time-travel. Few of them provide a plausible mechanism. For my story I would like to put forward such a theory.

We are all travelling forward in time at a 'speed' of 1 hr per hr. Suppose we would like to travel backwards in time at a speed of -1 hr per hr. What would have to happen?

My 'theory'

Note that this is intended to be science-fiction - I want to know what flaws it might have under the currently known laws of physics even if it is not based on evidence.

1. By Newton's First Law an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

2. We can consider time to be a dimension along which we are travelling.

3. There is no friction opposing our movement through time at a speed of 1 hr per hr.

4. By applying a force in the opposite direction to our direction of travel through time we can stand still in time or even move backwards (or of course faster forwards).

Can anyone refute this 'theory' by using a scientific argument or must I abandon it as a story element?

Notes

The necessary force would be measured in Newtons just like any other force.

The handwavery comes when explaining how the force is applied along the time dimension. Any vaguely plausible help with this would be appreciated.

I and my time capsule would experience our own time as going forward. The usual laws of thermodynamics would apply within the capsule. However, looking through the window I would see outside events happening backwards. Broken vases would lift off the floor, reassemble themselves and jump up onto the shelf, etc.

Paradoxes - I'm aware that many paradoxes still remain. I'll deal with those separately. At the moment I just want to consider the main idea.

• "Suppose we would like to travel backwards in time at a speed of -1 hr per hr. What would have to happen?" Well, for starters, thermodynamics must be proven to be fake news. Travelling backwards in time would see heat moving spontaneously from hot objects to cold objects, would see shards of glass jumping from the ground and self-assembling into bottles, would see carbon dioxide rushing in from the air and condensing into coal etc. (Not to mention that you must really really explain what is a "force" in this context; $F = m a = m \mathrm{d}^2 x / \mathrm{d} t^2$...) – AlexP Feb 11 at 9:48
• The problem is that it's well established that things don't move through time at one hour per hour. Your speed through time depends on your speed through space relative to the person who is measuring, and the strength of the gravitational field (or other acceleration) that you are experiencing. – Mike Scott Feb 11 at 10:44
• "Newtonian force": I reiterate. Newtonian force (mass times length divided by time squared) cannot possibly work, because it is dimensionally incompatible. – AlexP Feb 11 at 11:04
• What? Do you even know what the dimensionality of a physical quantity even is? The equation $e = m c^2$ is actually dimensionally sound. Energy has always been mass times length squared over time squared; one joule is by definition one kilogram times one meter squared over one second squared; it has always been so, since long before Einstein. – AlexP Feb 11 at 12:00
• @chaslyfromUK E=mc² is the theoretical energy stored in mass of the item or in other words: it is needed to get the mass defect between fusion and fission; the only theory that joins time and length into one thing is Minkowsky's, who invented quad vectors; also note physics.stackexchange.com/questions/122229/… – Trish Feb 11 at 12:28

Most of these answers are ignoring the tag and are comparing your system against "reality" and finding fault. Well... yes... we could do that... but that doesn't help you develop a suspension-of-disbelief system for your world.

I personally like the basic premise of your concept, but we need to introduce a better concept than "1 hr / 1 hr" because nowhere on earth do we analyze Newtonian action in the context of "1 km / 1 km." We analyze it as 1 Km/s.

And that's the basic problem. We're already using the time axis and no believable system can be developed based on unitless numbers. However, it appears the purpose of your system is to express time travel in terms of energy. Let's play with that for a second.

Arbitrarily, when walking down the street we can think of ourselves as using some number of joules to move our mass a kilometer down the road. What you want to do is use some number of "joules" (the temporal equivalent, let's call it the Chasly) to move our mass down the axis of time.

Temporal Rest Energy

If we sit in front of a TV and stare at it dumbly, we're moving forward along the time axis. It appears no energy is being spent — but in reality energy is being spent in your system just as energy is being spent by the Earth to move us around its rotation, around its orbit around the sun, around the sun's orbit around the galaxy, etc. There's all kinds of energy washing around. We'll call this "temporal rest energy" or ETR.

What units does this have? Time has two conditions here, so it's inappropriate to use "seconds" twice. What we have are seconds and traveled seconds. The former is the time during which energy is applied. The latter is the time traveled. E.G., it's a "distance" from the perspective of time travel. And since it's pretty much always true that increasing mass causes problems (and whenever "life" is involved, the inverse-cube-law is involved), I declare our fictional Chasly to have units of (sT * Kg3 / s2) because it's a form of acceleration (temporal acceleration dontchaknow) and it takes a lot of Chaslys to move a couch potato through time (prove me wrong OP!).

ETR = sT * Kg3 / s2

Now, what's important about ETR is that light, which is kinda massless1, experiences no forward time as it travels through the universe. Thus, the limit Kg as TST➝0 = 0. Photons have no temporal rest energy, which makes sense as they aren't experiencing time.

On the other hand, Couch Potatoes have substantial mass and definitely experience (if not notice) the passage of time. Thus, as TST➝1 (meaning a 1:1 correlation between time traveled and the time needed to travel it) the Temporal Rest Energy is equal to the mass of the Couch Potato cubed.

ETR = Kg3

Or, your average 150 Kg couch potato requires 3.375 mega-Chaslys just to experience the pleasure of watching TV.

Now, what does it take to stop the flow of time for that Couch Potato?

It takes a lot less for the couch potato to perceive time has stopped than it actually takes to stop time. So, "if it's truth you're interested in, Dr. Tyree's philosophy class is right down the hall." We're not interested in perception. We're interested in reality! (*cough*)

Newtonian Temporality demands that an equal and opposite force be applied. but what does that mean when we're dealing with time? We know our couch potato's temporal rest energy. Now we need to push against it. By applying -3.375 mega-Chaslys against the couch potato we are able to freeze said C.P. in place such that he/she/it isn't experiencing the passage of time. ET = 0, which is what we would expect since photons experience the same number of Chaslys and also experience no time. So far so good.

But what happens if we really try to move the mail?

Let's push our couch potato forward in time 60 seconds and take 4 seconds to do it!

ET = 60 * 1503 / 42 = 12.66 mega-Chaslys!

As we can see, the temporal energy needed to move through time increases the faster we want to do it! This simple reality can be proven by placing your head against a wall and trying to push through it. The faster you try to accomplish the goal, the more it hurts, thereby proving more Chaslys are required to move quickly through time.

OK, but did you answer the question?

I have no idea. I've been having too much fun. Give me a moment to check.... YUP! I think so! Except for calling the unit of energy the Chasly rather than Newton — which makes sense as it's a completely different type of energy, otherwise we'd call Coulombs, Newtons, and really confuse things.

1No it isn't. But, we're into science fiction and compared to me, the couch potato, it's so small that we'll call it zero.

• At last. Someone who understands the concept of science fiction :-) Actually it was my bad because I hadn't then discovered the tag alternate-reality. P.S. You have handily brought in the idea that constantly bugs me about time travel, i.e. that in fictional settings it always takes 'time' to travel through time. – chasly from UK Feb 12 at 10:02
• P.S. As I'm sure you are aware, C.P. does not in fact stand for Couch Potato but rather for the elusive Chronos Particle - the search is underway! – chasly from UK Feb 12 at 12:12
• +1 for an excellent SF analysis! – NofP Feb 14 at 16:00

Your theory is so full of flaws based on misunderstanding the basics of physics, that I will tell you how it is done by physicists.

## Real Time-Theory

We got a theory of time, and it is highly dependant on quad-vectors as they were developed in Minkowsky space:

• Vectors are not trinary but have 4 dimensions
• Time is a factor of this vector
• The notation is $$s=(t,x,y,z)$$
• Vectors need to be transformed between systems moving at different speeds, aka inertial frames
• Physics demands that $$-t^2+x^2+y^2+z^2$$ is invariant to coordinate changes between inertial frames
• This is called Lorentz Transformation
• The transformation between systems is dependant on the factors $$\gamma=\frac{1}{\sqrt{1-\beta^2}}$$ and $$\beta=\frac v c$$ whereas $$v=|\frac {ds}{dt}|=\sqrt{(\frac {dx}{dt})^2+(\frac {dy}{dt})^2+(\frac {dz}{dt})^2}$$ of the system based on its systems time (leading to t=const and conversely dt/dt=0) and c as light speed in vacuum.

As you see, force does not play any role in the basic time and time difference calculations between systems in physics.

## Force in time-theory?

Force is mass times change of velocity. Velocity is the derivate of space. So there is a way to calculate how one force in one system translates to a different one.

### Frames of reference - inertial frames

Think about this: if you shoot a bullet in the Y axis in a train moving in X axis, the bullet will travel on a straight path towards the train's frame of reference... but the world stands still while the train moves, and in the frame of reference of the world the bullet travels with both the bullet's own speed to the train and the train's speed to the world sideways, so a huge diagonal...

Ok, that was a non-relativistic example, but you see, that the speed of the bullet is higher in the earth coordinate system than in the train one.

### From speed to Force

Now, as the speed in the systems is different, the forces on items in these systems is different. Presume our shooter shoots at a sandbag on another train speeding along on the next rail. Both are in the same frame or reference. But if you shoot at the sandbag (after havign accounted for the sideways travel) hanging on the side of the tracks, and assuming that the mass of both is equal and the time they need to stop a bullet is equal, then the second impact is of higher force. Why? Because: $$a=\frac{dv}{dt}$$.

### Back to relativistic

Ok, we used a nonrelativistic example till here, but you just use Lorentz transformation and get the relativistic results. Which can be rather odd to normal understanding but perfectly simulate what really happens - if two particles speed upon each other with some relativistic speed, then the energy freed from the impact is different $$E_\text{nonrelativistic}=2\times\frac 1 2 mv - why? because you need to calculate relativistic energies, which get much higher due to the time dilation.

• This is easily the best explanation: to reiterate, that minus-sign in front of the t in the Lorentz transformations is pretty important in distinguishing time from any other spatial dimension. If you want to see what happens if that minus disappears, read Orthogonal by Greg Egan – neophlegm Feb 11 at 15:45

1.By Newton's First Law an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

2.We can consider time to be a dimension along which we are travelling.

3.There is no friction opposing our movement through time at a speed of 1 hr per hr.

4.By applying a force in the opposite direction to our direction of travel through time we can stand still in time or even move backwards (or of course faster forwards).

Can anyone refute this 'theory' by using a scientific argument [...]?

In Newton theory time is not a dimension in which one can move. You cannot cascade Newtonian dynamics to a domain for which it is not intended, unless you prove it still holds true.

Just look at the dimensions:

The necessary force would be measured in Newtons just like any other force.

Newtons are $$[kg \cdot m \cdot s^{-2}]$$. Your "time movement" doesn't include any length, so when you apply a "force" to time it should have the dimensions of $$[kg \cdot s \cdot s^{-2}]=[kg \cdot s^{-1}]$$ which is definitely not the same: it is a mass rate, useful maybe for measuring the consumption of an engine or the flow of a river, but not to "move" time.

This is a strong hint that the assumptions you have in place are not coherent with the premises of Newtonian dynamics.

• Okay so the force is [kg.s.s-2]. Isn't that just kg per second? If I can apply X kg/s along the time dimension that should do it (?) – chasly from UK Feb 11 at 11:26
• @chaslyfromUK no – Trish Feb 11 at 12:10
• @chaslyfromUK your name demands only 2 characters added ;) ok, I tell you no: Look at my answer. – Trish Feb 11 at 12:22
• @Trish - Yeah, I realised that as soon as I typed it! Thanks. I'm currently trying to understand your answer. – chasly from UK Feb 11 at 12:24

The general answer is for this theory of time travel to work objects like machines, vehicles, and people would have to undergo a process of time reversal. Once they had been time reversed time would be passing at minus one second per second.

T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal:

T : t ↦ − t .


T-symmetry can be shown to be equivalent to the conservation of entropy, by Noether's Theorem. But as the second law of thermodynamics does not permit entropy to be conserved in general, it follows that the observable universe does not in general show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold. However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium,1 contrary to their classical counterparts, although this has not yet been experimentally confirmed.

While a considerable body of physics is time symmetric, in their basic mathematical form, most physical phenomena are time asymmetric. To reverse time and enable this form of time travel to occur a hypothetical method of imposing strict time symmetry on matter would be necessary. This usually goes under the trade name of hurricane or typhoon strength hand-waving. To be applied with great care and caution and the warning of do not try this at home.

A forethought: it is a fact that extreme boredom seems to dilate time, while interesting and good moments pass by swiftly. We can postulate the existence of an interaction, called ania (i.e. boredom in Greek), which can alter the rate at which time progresses. The ability to perceive such alteration in time are due to peisma (i.e. stubborness in Greek), which opposes to changes to the rate of time flow.

I know what you are thinking: rate of time flow relative to what?

Relative to all universe configurations. For the hard-science-hatters, these could be quantum states. These configurations are like a gigantic graph, or a tree to be precise. In our world we like to place the big-bang as the root of the tree. In practice this is not necessary. At the moment we are travelling along one of the branches of this tree, away from the big bang. To travel across time is equivalent to move freely along the edges of this tree.

In our world, there is a precise between time and number of edges travelled. An simplified example could be that any choice that we have to make spawns a node with two edges going out of it along the positive direction of time. We pick one edge and continues until the next node. Time travelling would mean to go back to the node and be able to choose the other edge. Or go back further and choose an other branch entirely.

# Chronomics

## Laws

Chronomics is the field that studies the progression through time and the manners in which it can be altered. Similarly to classical dynamics, it is based on three laws:

First law: In an acyclical frame of reference, an object either remains at rest or continues to progress through time at a constant rate, unless acted upon by an ania.

Second law: In an acyclical frame of reference, the sum F of all anias on an object is equal to the peisma m of that object multiplied by the time contraction a of the object: F = ma. (It is assumed here that the peisma p is constant.)

Third law: When one body exerts an ania on a second body, the second body simultaneously exerts an ania equal in magnitude and opposite in time progression on the first body.

Interestingly. The third law seems to gives a simple line of investigation for time-travelling.

## Units

To satisfy Chasly's request of a strong parallel with classical dynamics, we just need to map the units of this system to classical netwonian units. Let's imagine that the tree-of-possibilities could be represented as an Euclidean object.

One meter along the edges of such tree could correspond to a Chasly-Number of universe configurations, like the Number of Avogadro represents the number of molecules in 1 mol.

Let me introduce the Chills, that is the unit for the number of edges visited in one second. Low chills indicate time dilation. Negative chills indicate travelling back in time.

1 Chill = 1 Chasly-number / 1 s = 1 m / s (recall that this is 1 meter on the tree-of-possibilities

### units for acceleration

m/sˆ2 = m * ( Chill / Chasly-number )ˆ2

m = kg

### units for force

kg * m/sˆ2 = kg * m * ( Chill / Chasly-number )ˆ2 = Netwon

# Final thoughts

Conjecture 1: Travelling back in time requires covering less edges than travelling to an alternative present. This also corresponds to spending less energy.

Conjecture 2: accelerating backward in time takes the same energy as accelerating forward in time (anias being equal in magnitude). However, the latter is a much more psychologically interesting experience because it has a positive number of chills.

Conjecture 3: The entropy at each node of the tree-of-possibilities is constant, with good peace of modern science.

Conjecture 4: All the travels along the tree-of-possibilities are already contained in the tree-of-possibilities. Somewhere among all the nodes, there is the entire path of your travels.

Proving these conjectures is left as an exercise to the reader.

You are traveling in a straight line along with the rest of the objects in the universe. Traveling back would mean two things. You travel and leave all the present objects that travel with you and end up in an now empty area of time, where you die as theres nothing to interact with. You might get lucky and travel into another universe using the same direction traveling in that same time and speed but you wouldnt travel back to a previous time in your own universe.

The second option is that you will travel backwards and find the "old" universe traveling in the other direction. This would mean that you immediately collide with your "old" self still traveling the other way. To keep traveling back in time you need to make every version of yourself go back in time for the same amount of time by pushing them all back. This will undoubtedly have consequences for the Timeline.

How about: If you go back in time, you travel backwards indeed, but into a parallel universe. This will dismiss all paradoxes which may result. Time may be defined as two-dimentional: 1st dimention is past/future, 2nd dimention is all the possibilities resulting from all the possible quantum states of all particles in the universe. The 2nd dimention is affected by your time travel and everything you do in an attempt to change events.

In other words, when you go back in time, your timeline splits into a parallel universe which diverges from the original one right at the "arrival" time. You will even meet your own parallel you.