Is Time travel Possible? (part 2 of 2)

Here is the conclusion of my interview for a popular science magazine: Science Illustrated in Denmark.

1:

Could you clarify why you find it highly unlikely that time travel is allowed by the laws of nature? Why do you believe, that the merger of general relativity and quantum physics leads to a theory (of everything) that will not allow time travel / closed timelike curves?

2:

When you build your own wormhole, you can only go back in time to the very moment a time loop was created. But couldn’t you – in theory - use an existing wormhole (if you have the technology to open a microscopic wormhole wide open) to go back further?

3:

Delayed choice quantum eraser experiments and the non-locality of quantum mechanics seems to indicate that the quantum world is “above” space and time. So, could we live in a world of self-consistently evolving quantum spacetime fields, which would work as a banana-peel-solution to the paradoxes?

1. Could you clarify why you find it highly unlikely that time travel is allowed by the laws of nature? Why do you believe, that the merger of general relativity and quantum physics leads to a theory (of everything) that will not allow time travel / closed timelike curves?

The answer is a bit complex and I’ll start with a detour. Quantum mechanics teaches us that position and velocity cannot be measured simultaneously with arbitrary precision. This goes under the name: Heisenberg uncertainty principle. Special theory of relativity shows that there is a maximum speed limit in the universe and nothing can go faster than the speed of light. Combining quantum mechanics with special relativity results in something completely new: creation and annihilation of particles (hence anti-particles). Why is this so? Suppose you try to pinpoint the location of a particle with arbitrary precision by putting it into a box and squeezing the box on all sides. By Heisenberg uncertainly principle, when the box is squished to nothing, because the position is known exactly, the velocity uncertainty goes to infinity and will be possible to have velocities higher than the speed of light. Since nothing goes faster than the speed of light, the higher velocity is only apparent because new particles are generated and we detect another particle instead of the original one. The theory for combining quantum mechanics with special theory of relativity is called quantum field theory and is the most successful theory of nature we have so far (the current measurement and prediction accuracy is better than a part in a billion). In quantum field theory, the lowest possible energy state is called the vacuum. Vacuum is not the absence of things, and it is a very violent place where virtual particles and antiparticles get created and eventually destroyed. Quantum field theory obeys a fundamental principle of physics called unitarity which means that information cannot be created or destroyed. A time loop violates unitarity because it can create new information out of nothing. When general relativity meets quantum mechanics, by time machine solutions, or by the simpler example of a black hole, unitarity is violated and information is no longer conserved. One may recall the debate between Leonard Susskind and Stephen Hawking on the black hole information paradox. The same thing is at play here and by its construction the best candidate for unification between general relativity and quantum mechanics, string theory, preserves information conservation and rejects time loops. If information conservation is violated, quantum field theory predicts that the universe is heating up and we simply don’t see this happening. Hawking also proposed a quantum field theory mechanism to prevent time loops. The moment general relativity is about to create a causal time loop, the virtual particles in the vacuum start traveling around the loop draining the energy out of it. The end result is that the time loop collapses. Since we lack the precise unified theory, Hawking’s computation is only speculative at this time.

2. When you build your own wormhole, you can only go back in time to the very moment a time loop was created. But couldn’t you – in theory - use an existing wormhole (if you have the technology to open a microscopic wormhole wide open) to go back further?

Yes in theory, no in practice. A wormhole has a delicate part, its “neck” which by general relativity will collapse very quickly unless it is kept open by negative energy. Think of negative energy as a credit card: you spend what you don’t have, and you have to pay it back eventually with interest (this is also because of Heisenberg uncertainty principle, but this time not for position and velocity but for energy and time). To keep a wormhole open for a decent amount of time, you need to keep feeding it negative energy and every time the interest compounds. Some extremely advanced alien civilization has to maintain the wormhole open for us to be able to see the extinction of the dinosaurs (like rolling the balance from one credit card to another credit card with a higher credit limit). And for that long amount of time, the energy required could easily exceed the entire energy of our galaxy.

3: Delayed choice quantum eraser experiments and the non-locality of quantum mechanics seems to indicate that the quantum world is “above” space and time. So, could we live in a world of self-consistently evolving quantum spacetime fields, which would work as a banana-peel-solution to the paradoxes?

This is correct. And this was shown in a precise mathematical way by David Deutsch using quantum mechanics. There may not be there any “banana peel” but it will feel like it.  However, this only solves the grandfather paradox. The lack of information conservation problem still remains and this is against quantum mechanics.

You can’t have the cake and eat it too:  you can’t have a quantum mechanics solution of the grandfather paradox while rejecting quantum mechanics because of lack of information conservation.

I think is safe to say that we all love “Back to the future” movies. I’d love to have a flux capacitor installed in my car and as a physicist I am saddened by the realization that time travel is almost surely impossible. However, physicists pursue time travel questions because they test the limit of our current understanding and the quest can provide hints of how to uncover the ultimate “theory of everything”.

Is Time Travel Possible? (part 1 of 2)

I will take a couple of weeks break from quantum mechanics to talk about the possibility of time travel. As it happens, I was asked a few questions for an article in the popular science magazine Science Illustrated in Denmark. The instructions were to keep the answers short, but I could add additional info to be used as seen fit by the editor. Also the explanation level should avoid being technical. This generated an interesting exchange which I will show in this and next post. Enjoy.

1:

Is it – in theory – possible to travel back in time? Does nature allow such time travel?

2:

If so, will it ever become possible to construct a time machine capable of transporting human beings back in time?

3:

And if this might be the case, how is paradoxes like the grandfather paradox prevented?

1, Is it – in theory – possible to travel back in time? Does nature allow such time travel? The answer to the possibility of traveling back in time is not yet known, but time travel is highly unlikely. Einstein’s general relativity theory – a very successful physical theory at large scale - allows many solutions which exhibit time travel but general relativity is at odds with quantum mechanics –a very successful theory at small scale - and so far there is no known physical theory which consistently combines them. There are several proposals being considered, like for example string theory, but only when such a theory will be validated by experiments we could have a definite answer to the possibility or impossibility of time travel.

Background info:

It is important to understand how time travel solutions occur in general relativity and what it means. Einstein’s general relativity equations are local laws and they do not forbid global behavior like traveling back in time. Since space and time are not rigid, they can be twisted and stretched by the presence of mass and if you continue doing it in certain ways, you can eventually manage to turn time back on itself. This is not unlike how one can turn a car all the way around in an empty parking lot. Then all sorts of paradoxes can occur and to understand them physicists studied for example how billiard ball games can be played in the presence of a time machine. To avoid paradoxes, the billiard ball may collide with its younger self in a self-consistent manner, but here is the catch: consider replacing the billiard ball with an egg. When it collides with its younger self it will go “splat” and create a paradox. The only way to prevent the paradox is for the egg not to break, and this means that: global consistency conditions required to avoid paradoxes imply non-physical local behavior and this does not agree with our current knowledge of nature.

2:

If so, will it ever become possible to construct a time machine capable of transporting human beings back in time?

The answer is a double no. First, assuming that time travel is actually permitted by nature, you can only go back in time to the very moment a time loop was created. In other words, nobody will be able to go back in time to witness the extinction of the dinosaurs, or the invention of the light bulb. Second, the energy required to bend space-time on itself is of galactic magnitude and you need to harvest the energy of an entire galaxy to bend space-time on itself. A more practical approach is by creation of a wormhole, but this requires negative energy and while negative energy is a real possibility, when you generate negative energy you have to pay it back with interest. To create a macroscopic wormhole large enough for a human to pass through you need yet again an immense source of energy.

Background info: The reason enormous amounts of energy are required is that gravity is the weakest force in our universe. Mass is equivalent with energy (E=mc²) and you are required to have a large amounts of mass (corresponding to even larger amounts of energy) to bend space and time. Titanic was hard to turn by a small rudder. Turning space-time all the way to itself is extremely hard with weak gravity. And how do we know gravity is a very weak force? After all it does not look that way when we fall for example. Consider a magnet on a refrigerator. The small magnetic attraction between the magnet and the sheet of metal can easily overcome the gravitational pull of the entire planet.

3:

And if this might be the case, how is paradoxes like the grandfather paradox prevented?

There are only two paradoxes generated by time travel: the grandfather paradox and creation of information from nothing. For the grandfather paradox there are two solutions: “the banana peel type solution” and the splitting the world into multiverses in quantum mechanics. Here is how they work.

In the grandfather paradox, you go back in time and you try to kill your grandfather thus preventing your own birth. But suppose at the key moment of the murder when you want to shoot your grandfather you step on a providential banana peel, slip and miss. And no matter what you try, there is always something which goes wrong and nature always conspires against you. Another solution is the multiverse idea in quantum mechanics. The moment you shoot your grandfather, the universe splits in two identical copies, one in which you fire the gun, and one in which you don’t fire the gun (call them universe A and universe B). The bullet from universe A jumps into universe B and kills the grandfather in universe B. Since that was not your grandfather in universe A there is no contradiction in universe A. In universe B, a bullet out of nowhere kills the grandfather which prevents your birth in universe B. But because you did not fire the gun in the first place there, universe B is also free of paradoxes.

For the creation of information out of nothing, the paradox goes as follows: As a young person you meet an old person who hands you the blueprints of how to construct a time machine. You work your entire life building it and as an old person you take the blueprints with you, hop in the time machine, and go back in time handing the blueprints to your younger self. So far there is no contradiction, but who wrote the blueprints in the first place? This paradox has no known solution.

Background info: As farfetched as it sounds, the splitting universe solution is actually correct and is based on real science. Splitting the universe in quantum mechanics is one of the several interpretations of the theory and since other interpretations are possible it can be taken as a narrative which can help visualize complex mathematical computations. The banana peel arguments may seem to contradict free will but here is a simple counterargument (I think originally given by Novikov http://en.wikipedia.org/wiki/Novikov_self-consistency_principle ): it is my free will to walk on the ceiling but the laws of physics prevent it.

Quantum mechanics in your face

Again

Two weeks ago I discussed the GHZ-M argument and I listed the exceptional talk by late Sidney Coleman. Today I want to revisit the strange nature of quantum mechanics and show how it violates common sense and classical intuition.  

This time I will present an argument introduced by late Asher Peres in his classic book: “Quantum Theory: Concepts and Methods” which uses the discrete measurement outcomes for spin.

Now I assume everyone is familiar with the idea that spin is quantized and takes only discrete values when measured. But what does this mean and why this is counterintuitive? Spin measurement can be done by a Stern-Gerlach experiment: 

silver atoms evaporate from an oven, pass through a velocity selector, then go through an inhomogenous magnet before hitting a detector. Classical physics predicts that the magnet causes the precession of the atoms and a vertical deflection in a continuous range from +μ to –μ (here I skipped the details of the derivation but please take my word for it).

But what is the experimental result? Only two deflection results are obtained and so “spin is quantized”.

But what is so special about it? What is special is that we can rotate the orientation of the magnet and still obtain only two outcomes because of the rotational symmetry. And this can generate a classical contradiction. Here is how:

Pick there orientations of the measurement direction, e1, e2, e3, 120 degrees from each other. By symmetry, e1+e2+e3=0 (here we add them as vectors). Now assume that the atoms have an intrinsic magnetic moment μ along a certain direction. In general the experimental outcome is computed classically to be the scalar product of μ with the particular measurement direction: e1, e2, e3.

Summing the outcomes we get: μ 1+ μ 2+ μ 3 = μ.(e1+e2+e3)  =  0 because e1+e2+e3=0 However, this means we are adding three numbers of the form +1 or -1 (the actual experimental results) to obtain zero and this is a mathematical impossibility.

The argument can be criticized because we are reasoning counterfactually and there is no experiment possible to measure all three simultaneously. In fact the three measurements are mutually incompatible. The contradiction still stands if (as Asher Peres put it) a measurement is a passive acquisition of knowledge. The strange world of quantum mechanics where objective reality does not exist before measurement is forced upon us by the humble discrete measurement outcome.

The Detection Loophole in Bell Test Experiments

Caroline Thompson's Chaotic Ball*

Continuing the discussion on Bell inequalities, supporters of local realism challenged the experimental verification by means of several experimental loopholes. One of these loopholes, the detection loophole, is very interesting because it can precisely reproduce quantum mechanics predictions in an EPR-B experiment.

The key idea is that spin measurements can have three outcomes: +1, -1, and no detection. In 1970, Philip Pearle found such an example and computed a minimum no-detection limit of 14% required to reproduce the minus cosine correlation, but the math there is cumbersome and it was not explored further. (What this shows is that detector efficiency needs to exceed 86% to close the detection loophole). I will not discuss Pearl’s model, but I will show instead an intuitive (but inexact) model found by Caroline Thompson in 1996 (http://xxx.lanl.gov/abs/quant-ph/9611037 ).

Let us start with the minus cosine correlation between spin measurement in EPR-B. In The EPR-B experiment, a source of two electrons initially in spin zero state emits two electrons in opposite directions and their spin is measured on two directions A and B making an angle α between them. In any experimental model (quantum mechanics, classical mechanics, and local hidden variable models) there are three fixed correlation values: -1 for α = 0, 0 for α = 90 degrees, +1 for α = 180 degrees. Quantum mechanics formalism and experiments show that the measurement outcome correlation is –cos α. But what is so special about this? When α = 0 by conservation of spin, if we measure the left electron on a direction and obtain an outcome, we naturally expect that if we measure the right electron on the same direction we obtain the opposite outcome.

However, the catch is in the slope of the correlation: since the differential with respect to α of –cos α is +sin α, the tangent to the correlation curve at α = 0 is zero. Let’s think of this for a minute of what it means: if we have a slight deviation in the two measurement angles, the correlation stays the same. In quantum mechanics this is true, because a Bell state is a superposition of two wavefunctions. So what? What this has to do with anything? In the classical case, the electron has a definite direction of spin independent of measurement and the correlation curve has a constant slope of 1 (the three fixed points are connected by a straight line). In quantum mechanics, the correlation curve slope at α = 0 is zero because there is a compensation effect in measurement outcomes due to superposition.

Now back to the detection loophole: can we imagine a simple classical system where not all measurements generate an experimental outcome, and still the correlation curve at α = 0 is zero? Late CarolineThompson came with such a simple system, and is as follows:

Consider a uniformed colored ball which spins randomly around its center. Pick two opposite points and write N and S on the ball (for North and South Pole). Let the ball spin chaotically and look at the ball from two different directions A and B and at certain time intervals. The two experimentalists write down what they see: N, S, or nothing.  If  the observers are close to the ball, due to the reduction in the field of vision, there are some bands on the ball which nobody can see and they generate the “nothing outcome”.

To compute the correlation, the experimentalists have to discard the cases where nothing was detected by one or both observers and the surprise is that the correlation exhibits a flat correlation curve at 0 and 180 degrees.

As I stated earlier the model is not exact, but it raises the question of the detector efficiency in experimental tests and questions the validity of the observed correlation as an argument against local realism because the observed correlations can be an artifact of incomplete detection. In general to create realistic models of the EPR-B experiments using the detection loophole (and exact models do exist) one needs to have unfair sampling depending on the angle between the measurement direction and the intrinsic spin direction. Since the undetected outcomes are by their very nature hidden from the experimentalist, who is to say that Nature obeys fair sampling? After all we want to describe Nature as is, and not to force our preconceptions of fair sampling on the experiments.

Do not expect however to prove quantum mechanics wrong by a few clever hidden variable models exhibiting the EPR-B correlation using the detection loophole. No experiment to date contradicted quantum mechanics predictions. Also in a few years it is expected that loophole free experiments confirming Bell theorem will become feasible.  

* I thank Richard Gill of making me aware of Caroline Thompson's work