Einstein and the speed limit of the universe

Einstein did not support the fundamental uncertainty of quantum physics. He stubbornly maintained the idea that reality was permanent and objective and that the observer played not a significant role. Yet the observer plays quite an important role in his best-known work, the theory of relativity. Precisely if you assume that the observer makes the observed ‘true’ and thus actually creates reality, his approach to the relativity of space and time offers a surprising outcome.

Special relativity

The special theory of relativity can be followed perfectly by using nothing more complicated than Pythagoras and a dose of high school algebra. But I’m not going to do that here now. There is a lot to be found on the internet doing that. Read for example: Special relativity math2410 from Leeds University.


An extremely important premise for Einstein was that the universe should basically look the same for two observers moving relative to each other. Ultimately, that’s a symmetry argument. Symmetry has been an important criterion in the theories of physics since Emmy Noether introduced it in 1918. He combined this criterion with the insight that the observed speed of light – in a vacuum – must be the same in all circumstances. This followed from Maxwell’s equations for electromagnetic waves and was indirectly confirmed by the experiments of Michelson and Morley who sought to determine the speed at which the Earth traveled through the supposed aether by measuring differences in the speed of light going in different directions with regard to this aether. The outcome was that they could not measure differences in speed, no matter how accurate their experimental set-up was.

To ride with a light wave

In addition, Einstein had realized from an early age that you cannot overtake or even keep up with a light wave. If you could keep up with light, Maxwell’s electromagnetic wave would no longer oscillate from your moving point of view, it would look like a frozen wave. But since the wave’s propagation is both caused and sustained by its ceaselessly oscillating fields, that couldn’t be right. Light must therefore always move at exactly 300,000 km/s for every observer. This follows also undisputedly from Maxwell’s equations because these do not contain any parameter relative to the position of the observer.

Einstein riding the light wave. The wave will seem frozen from his viewpoint. This is not possible. © Paul J. van Leeuwen

Einstein now imagined two observers moving relative to each other but who should both observe the same speed of light. Imagine a light source C standing still for observer Alice. Alice sees the light of C approaching her at c = 300,000 km/s. Observer Bob whizzes at great speed towards ligt source C, say 1/10 of c. Alice now considers that the light coming from C towards Bob must therefore move at 11/10 of the speed of light for Bob. I hope you can follow Alice’s reasoning. Otherwise, try to think of two cars driving towards each other while Alice watches along the roadside. Car with driver Bob drives at 10 km/h and car C drives at 100 km/h towards Bob and Alice. Car C here stands for the light that comes towards Bob and Alice. Alice observes (with radar) that the speed of car C is 100 km/h and that Bob and car C are speeding towards each other at 110 km/h. Now suppose that Bob would also perceive the speed of the oncoming car C relative to him as 100 km/h. That could only be if Bob’s clock ticked at 10/11 the speed of Alice’s watch. And not only Bob’s clock but also Bob’s entire perception of time would have to be slowed down so that Bob actually experiences the speed of car C as 100 km/h. In that case Bob will live a little bit slower. As far as Alice is concerned, Bob is now aging more slowly than Alice.

Time slows down and space shrinks

Now back to the light that is always experienced by every observer at the same constant speed. If Bob moves relative to Alice at 1/10 the speed of light and Bob sees the light move at 300,000 km/s, then that is possible if the time for Bob slows down by 10/11. Bob doesn’t feel that way because he himself is sitting in his delayed time capsule, his car.

This simplified estimate of the slowing of Bob’s time is not 100% correct because something also happens with Bob’s yardsticks, but what matters to me is that you get an understanding of relativity reasoning. If you want to do this completely right, then, as already mentioned, some algebra and Pythagoras are involved and the time dilation, the slowing down of Bob’s time, is described with:

Time dilation T for Bob’s clock moving at speed v relative to Alice’s stationary clock. T0 is the time of Alice’s clock. The closer Bob moves to the speed of light c, the slower his clock ticks as seen from Alice’s viewpoint.

Here v is Bob’s speed, relative to Alice (or Alice’s speed relative to Bob). If you enter here 1/10 of the speed of light c for v, then Bob’s clock turns out to tick 0.5% slower than Alice’s clock. Now we apply the principle of symmetry that Einstein argued. There is no absolute speed, speed is always relative. Bob, who experiences himself as stationary, observes Alice moving away from him at 1/10 the speed of light. So Bob also sees Alice’s clock ticking slower by 0.5%. This seems a paradox, but the theory is correct and has been experimentally confirmed in countless experiments. The solution is that Bob and Alice can’t compare their clocks until they come together and for that at least one of them has to turn around which means speeding up and slowing down. This breaks the symmetry.

You can see from the above time dilation formula that the maximum speed that applies in the universe is 300,000 km/s. The term under the radical becomes negative when v becomes greater than c, which would make the time dilation imaginary. That’s too bad because it makes non-imaginary trips to even the nearest stars impossible for us.

From Alice’s point of view, Bob’s rulers also shorten in the direction of his movement. For completeness, this is the formula for the contraction of fast-moving rulers, the so-called Lorentz contraction:

Lorentz contraction of a ruler L moving with speed v relative to the observer. L0 is the lenght of the ruler when at rest relative to the observer.

It goes without saying that this sparked a lot of discussion in the first half of the 20th century. Einstein took the position that the observers of the clocks and rulers did not play a vital role in relativity effects. According to him, they could just as easily be left out of the equations. Fast-moving clocks would automatically slow down, fast-moving rulers would shorten without the need for an observer. This elasticity of space and time and of the material objects therein was, and is still difficult to grasp but has been confirmed experimentally time and again. We, the physicists, are more or less used to it now, but we do not really understand it. It’s not natural.

Einstein fighting versus the probability interpretation of quantum physics

Einstein seriously put quantum physics on the map with his explanation of the photoelectric effect, for which he received the Nobel Prize. Light consists of particles with an energy per particle according to the Planck formula (f here stands for the frequency):

Planck’s law: the energy of a quantum of radiation energy is propertional to its frequency and is inversely proportional to its wavelength

But after that he argued vigorously against quantum physics and especially its implications, to no avail. Especially against the probability interpretation of Bohr, Heisenberg and Born: that the state wave, the solution of the Schrödinger equation, represents the probability that the particle will be found at a given location and time when measured. That went against Einstein’s gut view of the world as an objectively permanent collection of material objects. Einstein’s objection is understandable if you adhere to the materialistic view of the world, because a probablity is not an objective material object. It is something that exists in our mind. A thought.

And that’s exactly my own idea of how the universe works. Everything we experience takes place in the mind. The perception of the measured particle thus becomes identical to the thought of it. The experience is then the same as its creation. That explains to me very well why the laws of physics behave according to mathematical formulas. That is something that many physicists, including Einstein, have expressed their amazement about. So the observers’ mind plays an indispensable role in the universe, it creates it. Mathematics is something of and in the mind. The mind uses apparantly mathematics in its creation of the universe.

Time and space are concepts of the mind.

That idea suddenly makes things like the slower passing of time, the shrinking yardsticks and the curved space of general relativity, much more palatable. In a dream we would really not notice these things either. There exists no real objective time outside of us that does slow down, there is no objective space outside of us that does shrink, it’s all happening in the mind of every observer.

Science Fiction?

That offers hope for the possibility of exploration of the cosmos. The maximum speed in the universe that we observe – that of light – seems to be something that the mind has imposed on itself. But as soon as we can accept that time and space is happening within the mind, the possibility opens up that we could move through the universe beyond that limitation. Traveling within the mind is not bound by the restrictions of relativity. This, I believe, is also the correct interpretation of entanglement and instantaneous action over long distances, as confirmed by all those Bell tests. Traveling through the universe by means of the mind could even be the way – one that intelligent beings existing elsewhere in this vast universe already have discovered – to travel through the cosmos despite Einstein’s speed limit. And to visit us. Experiments have already been conducted confirming that quantum tunneling shows speeds greater than that of light.

A universe like a slowly fading flare

That the universe is a creation of the mind also offers an alternative for the pending entropy death of the universe that physics has been predicting for a century and a half now. Even if that is a immeasurably distant future away, it remains a bleak prospect contradicting any sense of purpose of the world. What was that fantastic spectacle all for if that is to be the end? But if the universe is the product of the creative mind, then that is by no means an unavoidable end to everything. On the contrary.


What I want to say with this story is that there is a good chance that two apparently incompatible theories – relativity and quantum physics – can be merged together very well when we start to include the all important role of consciousness. The intelligibility of the nature of reality would only increase as a result.

Epicycles and quantum fields

Feynman diagrams

Feynman diagrams are used by physicists to represent the possible interactions between elementary particles.

Wikipedia: The lines in Feynman diagrams represent particles interacting with each other in some fashion. Mathematical expressions correspond to every line and node. The probability of certain interactions occurring can be calculated by drawing the corresponding diagrams and using them to find the correct mathematical expression. The diagrams are basically accounting tools with a simple visual representation of an interaction of particles.

So it is not the case that physicists assume that those particles exist physically during their lifetime and that they follow trajectories. That contradicts the wave aspect that quantum physics assigns to them. They prefer to assume that the particles in some virtual way do ‘try out’ all possible paths, where one is always chosen and becoming physical on measurement. Each Feynman diagram is just a way of visualizing one the possible interactions. But the temptation to view these interactions as objective physical events is strong.

Feynman diagram with two electrons and one single foton for repulsive field interaction

The above figure is one of the simplest Feynman diagrams you can find on the internet. Shown vertically is the time (t), horizontally the position (x). This diagram shows the simplest way two electrons can affect each other. Two electrons fly towards each other, repel each other at time t0 and fly apart again at the same speeds. At the moment t0, when they are at positions x1 and x2, they exchange a photon. A photon carries a certain momentum, transfers it and thus exchanges the momentum of both electrons. After the exchange, the electrons fly apart at the same speeds at which they first approached each other. The question is, of course, how electrons ‘feel’ that there are other electrons nearby so that they have to exchange photons. The exchange, as shown here, is an instantaneous process, the path of the photon is horizontal at t0.

The photon exchanges the electron momenta

Hey, that’s curious, that makes the speed of the photon infinite. That will certainly not be the intent of the diagram. However, there is more that raises questions. The direction of the photon is not indicated. The photon could move from right to left as well as from left to right. The electrons both undergo an momentum change due to the exchange of the photon. Momentum is the amount of movement expressed in mass m times velocity v: p = mv. The left electron undergoes a velocity change Δv1. From this follows a momentum change Δp1= mΔv1, ditto for the right electron: Δp2= mΔv2. The velocity changes Δv1 and Δv2 are of equal magnitude and of opposite direction: Δv1 = -Δv2. This means that the total momentum does not change: Δv1 + Δv2 = 0 so Δp1 + Δp2 = 0. That is 100% according to an important law in physics: The total momentum of a closed system does not change.

The accounting is correct for the momenta

The photon does the transfer of the momentum, because a photon carries a momentum according to De Broglie: p=h/λ. Both electrons undergo an equal and opposite momentum change which is transferred through the photon, whether the photon moves to the left or the right. For example, suppose the photon moves to the right. The left electron undergoes an impulse change Δp1= mΔv1 = h/λ, the right-hand electron Δp2= mΔv2 = – h/λ. This last minus sign is because the photon loses its momentum when interacting with the electron on the right. Since v1 = – Δv2 holds, the total impulse Δp1 +Δp2 is preserved. If the photon travels in the opposite direction, the result is the same. So it doesn’t matter in which direction the photon moves. If the photon has the speed of light, then the impulse changes will be slightly consecutive in time. The emitting electron changes its momentum first in time, the receiving electron a little later. But that’s not a real problem. The accounting of the momenta is correct.

At least two photons are needed.

But what about the energy? A photon also carries an amount energy that is proportional to its frequency f: E=hf. That’s Planck’s law. If the photon moves to the right, the left electron must have lost some amount of kinetic energy because it has transferred it to the flying away photon: ΔE= – hf. As a result the electron on the left has lost some kinetic energy. The receiving right electron then receives this energy as gained kinetic energy. So it has a higher speed. And if the photon were to move to the left, the right electron loses the kinetic energy that the left electron gains. That can’t be right. Both scenarios conflict with the elastic collision of two objects and cause an asymmetry in the course of the interaction. If we want to achieve the same as in an elastic collision we must assume two simultaneous photons, one going from left to right and one from right to left. Both transfer energy and impulse. This way the accounting is correct again. The sum of the transmitted impulses is zero and there is no transmitted kinetic energy. We need two photons for that. In itself, a Feynman diagram can be supplemented in this way. There is no objection to that.

Feynman diagram with two electrons and two photons for complete repulsive quantum field interaction

There should be a simpler story

A correct story with the exchange of photons becomes considerably more difficult with particles that attract each other, such as an electron and a positron. Isn’t it actually simpler to assume a single interaction in which the charged particles exchange their momentum but no energy? In my opinion, a photon is nothing more or less than the observation of an energy exchange that must have occurred. The assumption that it should be a physical particle is the result of the image imposed on us by classical physics. A photon can therefore also be regarded as nothing more than the observation of an impulse exchange. Elsewhere on this website, and also in my book, I argue extensively that the photon does not physically exist and thus does not travel. The photon is, I think, a reified abstraction.

Quantum field theory

In quantum field theory it is assumed that a moving electron, which is a non-physical probability wave as long as it is not measured, is surrounded by a cloud of virtual (!) photons, where two of them become real photons in this case, to take care of the momentum exchange . This representation replaces Maxwell’s electromagnetic field concept. Actually Maxwell wasn’t very happy with his field concept since he had to assign properties to empty space. Quantum field theory now replaces that electromagnetic field by assuming large amounts of virtual photons popping in and out thin air. In this way you avoid the troublesome idea that electrons would have ‘feel’ each other’s proximity and decide ‘in time’ to perform an impulse exchange in order to move away from each other again. In this way the objective electromagnetic field has been replaced by something even more complex and ultimately based on the field concept, a state of empty space, this time chock-full of virtual particles. Admittedly, quantum field theory does provide very precise predictions. But that could also be said about the epicycles of Ptolemy.

A mini Big Bang in a mini universe of billiard balls

Virtual dancing with quantum fields, a dream

Before 1900 we had the rather simple billiard ball model of the universe. Quantum field theory has now taken its place. To get an idea of its message let’s assume that you’ve been worrying deeply about quantum fields and those virtual photons. Exhausted you fall asleep and you start dreaming. You find yourself in a dance outfit on a huge expanse of ultra smooth dance floor where you can’t see the walls. Everywhere people are dancing, it is swarming with them in some places. In quieter places you see someone alone doing a pretty good pirouette. The floor so slippery that there’s no way you can move from your place. How do the others do that? Then you notice that billiard balls are constantly appearing and disappearing everywhere in the air. The heavier the ball, the faster it disappears again. The smaller and lighter ones last a little longer but eventually they disappear too. You understand that those balls are virtual but that they are physical for a short time. Now you understand, you want to dance and you are looking for someone to dance with.

Then you see someone repulsive sliding towards you. You don’t want to dance with this person. So, you grab a large heavy virtual billiard ball, that just appears in the air near you, and you throw it in this person’s direction. The other person catches the ball neatly after which it immediately disappears again into thin air. The result is that you two are sliding apart again. Then you see someone really attractive. You want to dance with that person, but the person is gliding along a trajectory that does not come close to your trajectory. So, you grab another billiard ball, that conveniently pops up at that moment. You throw the ball in the opposite direction and you see to your pleasure that the other person does the same. You move towards each other and begin to dance happily … and then you wake up. End of dream. Regrettable.

But you now suddenly understand the idea of ​​the quantum fields a lot better. It’s just the old billiard balls story again. But now they are ‘virtual’. Virtual is a concept from optics and means that an object exists physically but not physically, it is not tangible. A rainbow is a virtual object. You can’t grab it but materialistic thinking tries to do just that.

Virtual epicycles

When I think about this tortuous explanation with virtual photons, it inadvertently reminds me of the epicycles of Ptolemy that ‘explained’ the movements of the planets in the heavens in a very complex way and that lasted for 1400 years because the idea of the earth at the center was something people preferred rather strongly and, more important, because it was so accurate in its predictions. Take a look at the Ptolemaic animation of the movement of Mars through the heavens below to get an understanding of its utter tortuous complexity. Ptolemy’s epicycles were indeed virtual.

The Ptolemaic model of the solar system. The Earth (blue) right next to the center of the deferent, the great circle. Mars moves around the Earth in epicycles, small circular orbits whose center moves across the deferent in a year. The yellow ball is the sun as it moves through the zodiac in a year.