Endgame: Was it really Avenged? A Quantum Mechanical perspective

“All we can do is our best and sometimes the best we can do is to start over” - Peggy Carter

It seems that we should start taking the words of our significant others seriously now since one never knows at which point in time their simple statement can become a lifesaving tool for the entire Universe. I am pretty sure when Ant-Man had proposed his “time heist” theory to start over, Steve’s heart would have skipped a beat. So, indeed there was a solution to bring everyone back from decimation.  Steve Rogers et al., should they choose to accept the mission, had to travel back in time through the quantum realm, collect stones and simply snap their finger. A perfect, happy ending to 22 interconnected movies and 11 years of effort. But the only problem is that quantum mechanics is a bit more complex. And is why We Need Heroes, isn’t it!

Our heroes with their motto:

“If we can’t protect the earth, you can be damn well sure we will avenge it”

decided to pull off one last one whatever it takes, with stakes of saving the entire universe against the wrath of Thanos, the dogmatic leader of Malthusian economics. But did our heroes really win? Was the universe really avenged? Quantum physics actually agree to disagree.

Einstein’s theory of relativity works well in describing objects at large scale. However, as Scott Lang and Tony Stark had described, objects behave very weirdly at the sub-atomic scales (quantum scales). Quantum physics deals with the understanding of this smallest part of the universe, which is one of the biggest mysteries. String theory (sometimes called the theory of everything) is a unifying theory that reconciles the differences between quantum theory (laws of the small) and the theory of relativity (laws of the large) to explain all known forces and matter. But, interestingly, for it to be mathematically consistent, the theory posits the existence of a 10-dimensional universe. Physicists suggest that these additional dimensions might exist curled up at ultra-microscopic scales which are not visible to us. The plank scale is so small that I can’t type that many numbers of zeros, it’s in order of 10^-35 metres. But no worries, Marvel has Doctor Hank Pym to resolve this issue. Through the use of Pym Particles, our heroes can shrink themselves to these scales and exploit these extra dimensions. But other than 3 spatial dimensions, which one should one choose?

Using the mathematical properties and physics, extra dimensions can be visualized. We all know the 3 spatial dimensions. The 4^th dimension is considered temporal, while the other 6 are considered spatial. As Einstein had suggested and has been quite agreed upon, that we do live in a fabric of space-time, that is, in 3 dimensions of space and 1 dimension of time.

Before jumping to visualize higher dimensions it would be advantageous to understand that one step higher dimension enables an individual to teleport from one point to another in one’s own dimension. For instance, curling up the 2D world through the 3^rd dimension would connect any 2 points in the 2D the plane, thus allowing teleportation in the 2D world (as shown). Suppose an ant needs to travel from point A to point B in the 2D plane. It can do so by traversing along the 2D plane from point A to point B. However, if we curl the 2D space through the 3^rd dimension, the ant can now move from point A to point B within a blink of an eye. Thus, the ant used 3D space to teleport from point A to point B in the 2D plane.

In a similar manner, the 4^th-dimension allows teleportation in the 3D space. Remember the space stone, the tesseract, which allowed Thanos to roam around and destroy our cosmos during the infinity war. Well, he could teleport because the tesseract curls 3D space through the 4^th-dimension. The present visualization of 4D structure actually comes from the original works of an architect, Claude Bragdon, who in his book A Primer of Higher Space in 1913, first proposed, what has now been accepted as a representation of the 4^th-dimension equivalent cube or the tesseract. The figure below (left) is the digitalized copy of Claude’s book which shows the tesseract. And the figure below (right) is the one that Tony Stark had found in Howard Stark’s notes in Iron man 2. Interesting isn’t it! In a nutshell, tesseract allows one to teleport in the 3D space by curling into the 4^th-dimension

The 4^th-dimension, as said before is a temporal dimension. Had one been the 4th-dimensional being, the individual would be able to witness its own birth and childhood at one end and its old age and death at the other end, and all at the same instant (as shown below).

But since we are 3D creatures, so like the 2D flatlanders we only witness the 3D cross-sections of our 4^th-dimensional self. Now, this is where time stone rolls in. An individual owning the time stone actually becomes a 4th-dimensional being. It is for this reason that the Ancient One and Doctor Strange knows all about the future and the past. They can witness the entire life of anything in the form of an undulated cord (as shown in the figure above). It is for this reason, the Ancient one had said to hulk during the battle of New York, “you are a bit too early. Stephen Strange is currently performing surgery about 20 blocks that way”.

Remember in order to teleport from one point to another in one’s own dimension, the individual would be required to use one higher dimension. Therefore, to travel in the 4^th-dimension, one would need to curl the 4^th-dimension space into the 5^th-dimension. So, the 5^th-dimension would allow an individual to travel in time. The figure below (leftward) shows the 2D geometrical projection obtained using the formal equations of a cube in the 5-dimensional space, whereas the figure below (rightward) shows doctor strange using the time stone. Similar isn’t it!

                                          

QQuantum physics describes everything as waves, an abstract mathematical wave, which can be thought of as a wave of possibilities. Quantum mechanics support the probabilistic nature of the universe as opposed to the deterministic nature suggested by Classical physics and supported by Einstein. According to quantum physics, the act of measurement or observation collapses the wave of possibilities, but if one does not observe then all the possibilities exist.

Thus, the 5^th dimension is the plane of all the possibilities. Each of us is only collapsing the indeterminate wave of probable futures contained in the 5^th dimension into the 4^th dimension that we experience as time.

So, before Thanos’s snap, broadly speaking, quantum mechanically, the world was in the superposition of |Thanos winning> and |Thanos losing> and both the possibilities existed in the 5^th dimension. With infinity war, an act of observation, Avengers lost, collapsing the wavefunction towards decimation. It is also for this nature of quantum mechanics that Doctor strange had said to Tony during the Endgame, “if I tell you what would happen, it won’t happen”, because measurement collapses the probabilistic wave. Thus, “they continued to move on” in the 4^th dimension with decimation.

Now, this is where the main plot of Endgame comes in. Scott Lang had suggested, ”what if there was a way in which we could enter the quantum realm at a certain point in time and exit the quantum realm like before Thanos”. According to the physics of time travel, what Scott had suggested is to travel back in the 4^th dimension through the 5^th dimension, grab the stones, snap their own figures and thereby travelling the other 4D line towards no decimation in the 5th-dimensional plane. This process could have been cut short if they had a machine that would allow them to travel in 6th-dimensional space. This is so because the 6th-dimensional space would allow an individual to teleport in the 5th-dimensional plane. Thus Avengers could have travelled directly from the decimated universe to the non-decimated universe in a couple of minutes, The End! But, the time machine allows travel in the 4^th-dimension through 5th-dimensional space, and therefore they had to take the long route resulting in a 3-hour long movie. 

Endgame actually had two portals for travelling in time, one developed by Hank Pym and the other by late Tony Stark. Pym’s time machine uses quantum mechanics, shrinking oneself to the plank scales and using the hidden 5^th dimension as proposed by the string theory. Tony’s time machine, on the other hand, uses Einstein’s relativistic equations and wormhole’s concept, to perform time heist in the 5^th dimension.

Since Tony’s time machine was the highlight of Endgame, the one which gave them the chance to take all back, let’s have a reality check by looking at physics behind such a machine.

Time travel into the future is very much possible and agreed upon. The mechanism to travel into the distant future is to use the time-dilation effect of Special Relativity. It states that a moving clock appears to tick slowly as it approaches the speed of light. This effect indeed applies to all types of clocks including the biological one. Thus from the viewpoint of physics, if one can build a spaceship, overcome engineering hurdles and travel at relativistic speeds (realistically one may use the gravity assist of black holes as in the Interstellar) one can very much travel into the future without breaking any laws. It is the travel into the past which turns the tables upside down.  

The solutions of Einstein’s theory of General Relativity known as Closed Timelike Curve (CTC), describe trajectories through spacetime that allow for time travel to the past without acceding the speed of light.  The problem is deciding whether these solutions represent situations that could occur in the real universe, or whether they are mere mathematical oddities incompatible with known physics. To render a time travel model, one needs to manipulate matter and geometry of space-time in such a way which creates a path that circles back in time. This model on the paper would require geometrical properties of the Mobius Strip, as was used by Tony. If you take a Mobius strip and draw a line down the length of it, the line would eventually be on both the sides of paper before it meets itself. It appears somewhat amazingly that the strip has only one side. So if a 2D individual travelling down the line you just drew (the leftwards figure as shown below), it would end up at the same point without even feeling that it had left the 2^nd dimension. Its perception of the journey would be like the one shown by the rightwards figure below. In reality, it would actually be looping and twisting through the 3^rd dimension. The similar loop for a 3D being could enable twisting and loop through the 4^th dimension. The closed timelike curve could not use a simple cylindrical geometry since it creates time paradoxes like the grandfather paradox. Mobius strip, however, does allow one to deal with such paradoxes.

Since we are Marvel Fans, let’s call our version of the grandfather paradox as the Nebulae paradox. Suppose, Nebulae in 2023 had an epiphany that she had done wrong things in the past and blames herself for assisting Thanos which dusted half the universe. So, Nebulae decides to travel back in time and kill herself in 2013, supposedly the time before Nebulae tells Thanos some valuable information about the stones without which Thanos would have failed. Therefore, Nebulae travels from 2023 to 2013 and kills herself in 2013. Running down that timeline of the universe, if she had been in a cylindrical time loop (the leftward figure), she would be travelling back in time again in 2023 to kill her own self in 2013. However, Nebulae was already killed in 2013 so there would be no Nebulae to travel back in 2023 this time or to kill. Thus a paradox!

Now on the other hand, if there were a Mobius time loop, then when Nebulae would have travelled back in time from 2023 to 2013 and killed herself, she would have actually entered the alternate universe. Look at the difference in the way these strips connect the time loop as marked by the red coloured edges. Mobius the strip does allow for the alternate universe to exist and so Nebulae upon killing her own self in 2013 moves to an alternate universe, the left side of the strip, which does not have Nebulae and there is no arrow for time travel. In this way, the Mobius strip allows time to travel without paradoxes.           

When this model is converted into an actual machine, it would have topological features of a wormhole. The wormhole is basically a tunnel connecting spatially separated regions of space-time. It is claimed that wormholes can be used to create closed timelike curves. Giving one mouth of the wormhole a substantial velocity (thereby dilating time) with respect to the other would then allow passage into the past. It was this time dilation at plank scale which eventually opened the possibility for our Avengers to perform time heist. The dilation can be realized by the fact that plank time is of the order 10^-44 seconds. The theoretical properties of wormholes have been extensively studied over the past decade but little is known about the way to form a macroscopic wormhole. The gravitational fields required to make a macroscopic closed time-like curve would have to be very strong, and manipulating them would have to be very precise.

Now coming to the main question if the universe was Avenged? In fact, NO. As Hulk had said to Rhodes, ”if you travel to the past that past becomes your future and your former present becomes the past which can’t now be changed by your new future”. This is true indeed. In the physics of time travel, this is called as the Novikov self-consistency principle. The principle asserts that if an event exists that would cause a paradox or any "change" to the past whatsoever, then the probability of that event is zero. It would thus be impossible to create time paradoxes. So, even if our heroes do go back in time and alter the events somehow, they won’t change their present timeline in which decimation occurred. In fact, they would jump into an alternate universe, an alternate reality which arises from the Deutsch’s (which was also mentioned by Tony Stark) many worlds interpretation of quantum mechanics. So, as was discussed earlier, both the universe’s, the one with decimation and the one without decimation exists and changing the past would not change their own timeline in which events had taken place but only would take them to an alternate timeline. What Avengers did was quit their own universe, the sufferings, and jumped to an alternate one. The people who had lost their loved ones, their families in that reality will not get them back. What’s been done has been done. That timeline would always be half empty. Upon scrutinizing, in a way, this is what was explained by the Ancient One about the flow of time. So, when Cap went back in time and put all the stones back at the same time they were taken, it was made sure that the timeline of the infinity war is indeed intact and so in that alternate reality decimation has been confirmed. Looks like Avengers adopted the path of escapism. This has increased the importance of Thanos’s line manyfolds – “you could not live with your own failure. Where did that bring you? Back to me”. Indeed Thanos is right!

With the Endgame, Marvel has opened up its multi-verse. In the newly created reality by the Endgame, several new possibilities have reopened. For instance, one might think that in this world, Loki might still be alive since he escaped after the battle of New York using the tesseract when Tony’s plan failed. But was he. Maybe not. This might be the reason why Endgame had shown Loki being locked up in Asgard in 2013 when Thor had gone back to get the reality stone. Somehow he might have been caught again and locked. Or maybe in 2012, Tony did create an alternate reality where Loki manages to escape. There is a multitude of possibilities, but let’s leave it to the Marvels “What if…?” series.

From my viewpoint, keeping the self-consistency principle and the many-worlds interpretation in mind, there would exist a reality in which despite Avengers travelling back in time, they fail to gather infinity stones. However, some part of the story might remain the same, that is, even in that reality, Thanos, scans Nebula’s memory and in this way becomes aware of the location of all the infinity stones and successfully gathers all of them. This reality and this timeline might be the one that was shown in the infinity war, perhaps it’s later part. And since Thanos in that reality would have seen his future, having already scanned Nebula’s memory in this own past, that might explain why he greets tony and says, “you are not the only one cursed with knowledge”. Maybe Thanos was referring to this instance where Thanos knows about the future but the Avengers do not. It might be for this reason that Thanos indeed won the battle of Wakanda. In fact, in the infinity war Thanos does not attempt to kill any of the Avenger himself but Tony, since he knew that Tony might be the one who can be a real threat and is capable to decimate Thanos himself.

The take-home lesson for us should be, firstly, as Tony’s dad had said, “No amount of money can buy a second of time”. Secondly, in 3 words - Marvel is marvellous!

Love you 3000…

[P.S. - check the total number of words in the article ;)]