Quantum entanglement is generally presented as the effect that if two (or more) quantum objects have a common history that they are quantum entangled until one of them is measured. Common history means that they have had physical interaction in the past. That is, the objects have one common quantum wave and, if one of the objects is measured, its collapse has an immediate influence on the properties of the other entangled objects. This has been demonstrated time and again in numerous Bell experiments that seem to convincingly demonstrate effects that are contrary to the laws of relativity. These say that the maximum speed of information transfer is the speed of light. For more on entanglement see this page on this site.
Entanglement in time
In 2013, an experiment was conducted – Entanglement Swapping between Photons that have Never Coexisted – that showed that photons can become entangled even when they have never been together. What does that mean? A somewhat clearer way of describing the experiment is ‘entanglement in time instead of space’. See the diagram below from the publication of the experiment.
Four photons exhibit a common quantum wave that starts with the creation of the first photon entangled with a second photon because they were created as pair. The first photon is measured, irrevocably thereby ending its existence. The second photon is then entangled with one of a second pair of photons that are created later in time than the destruction of the first photon by its detection. Finally, photon four, the second of the second pair, is measured. The measurements of photons one and four have been shown to be correlated. Which means that all photons were indeed entangled.
Their entanglement, a common history, happened via entanglement of photon two and three. This was done by a Bell projection where these two photons were detetected after passing through a Bell type polarizer with two inputs and two output channels. I can’t explain this further here, because I’m not really familiar with this technique. I therefore refer quantum physicists wanting to know more to the publication of the experiment. The conclusion the authors draw from the outcome is that photon one and four were entangled while the existence of photon one ended before photon four was created. So, they evoked and observed entanglement in time, not in space.
Explanation of the diagram:
I: The birth of entangled photons one and two at t=0.
II: The destruction of photon one by its detection.
III: Birth of entangled photons three and four.
IV: Bell projection of photons two and three. This will make these photons to become entangled. Because photon three has become entangled with photon four, all four photons have become entangled, even though photon one no longer exists.
V: Detection of photon four.
VI: Observation of the result by observer!
The results of the detections of photon one and four are of course only viewed after photon four has been detected. Only then is the result ‘experienced’ in the experimenter’s awareness. That’s important in this regard.
This is strongly reminiscent of the retrocausal effects that occur in the delayed choice experiments and about which heated discussions can be found on the internet. As I note at the end of the post Schrödinger’s stopwatch, the Copenhagen interpretation of quantum mechanics implies that observation (measurement) causes the spatial manifestation of the quantum object through the collapse of the quantum wave. Our looking inside the box not only manifests its contents in space, the radioactive atom, the stopwatch and the Geiger counter, but also manifests the stopwatch with the clock pointer indicating a specific moment in the past. This implies that these three observed entangled objects are not only manifested in space but also in time.
But that is, in my opinion, only apparent retrocausality. I think, it is the literal creation of history through the observation of an observer carried out at a later moment in time. It has always been clear that any experience of ours always lags behind what the experience tells us now. In most cases, the distance to the interpreted past is small, otherwise we would never be able to respond adequately to the world. But however small that distance may be, our experience is always an interpretation of a past event. We are always lagging after the PRESENT. We live however in the past.
Consensus in a virtual reality
Observation thus records an event in the past. After that, the result cannot be altered any more. The past, after observation, is fixed. In my book I make a case for the view that our experienced world is only an experience that takes place entirely within the mind. A virtual experience. But then the question inevitably arises how it is that we can usually agree with each other about our experiences. This is ensured within this virtual reality by recording everything that is observed as fixed history which can no longer be changed. The experimenter who first looks at the results of the experiment irrevocably records what happened. After that, the others can only confirm this. That is not true retrocausality but the creation of history. Creative accounting.
"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."
"How can it be that mathematics, being after all a product of human thought, which is independent of experience, is so admirably appropriate to the objects of reality?"
1905 – The end of the Newtonian Universe
The publication of Albert Einstein’s special theory of relativity in 1905 should have marked the end of the Newtonian view of reality as a stage made up of permanent unchangable objects. Quantum physics just emerging at the time would further undermine that image. Yet apparently that end has not yet really sunk in. Many scientists who are not very skilled in physics still use the old billiard ball model of the universe as the model of reality
Special relativity is a special case of general relativity – also called the theory of gravity. This special relativity is a theory about observers moving uniformly with respect to each other – that is, without accelerating or decelerating – in which gravity plays no role. In order to achieve some understanding let’s put Alice and Bob back on the scene. That’s a bit easier to follow.
Each of those two will experience and also regard itself as at rest while the other is moving. Each will find that the other’s clocks run slower than their own one and that the other’s rulers are shorter than their own ones. This effect becomes larger as the difference in speed increases and only becomes noticeable when the difference comes close to the speed of light. But these differences are in principle always there. If Bob is standing along the highway and sees Alice driving past at 100 km/h, Alice’s clock will slow down from Bob’s viewpoint and her car will have become shorter. As far as he’s concerned, Alice has also gained a utterly tiny bit of weight. But Alice does not speed up or slow down, she considers herself and everything in the car at rest, and sees Bob passing by at 100 km/h. For her, Bob has gained a little weight, Bob’s clock runs slower and his waistline is shorter than when they walked an hour ago together.
Space becomes curved by the presence of mass and according to the general theory of relativity we experience curved space as gravity . The image below attempts to clarify that effect – in vain as far as I am concerned. The mass of the earth distorts the two-dimensional texture of space. However, we live in in three dimensions and we cannot image a fourth dimension to make curves in three dimensional space. On top of that, to explain the dent the earth makes in the two-dimensional texture of space you still need gravity pulling the earth down. But mathematically it all makes perfect sense.
‘These relativistic effects are not an illusion’ did a physics teacher assure us in a course in 2018, ‘They are real’. Relativistic effects have indeed been confirmed experimentally. Any GPS device has to take into account that the clocks in the satellites are running faster than on ground level – 38 microseconds faster in 24 hours. Also think of particle accelerators like the Large Hadron Collider in Geneva, where protons travel in an underground circular tunnel with a diameter of 8.4858 km at 99.996% the speed of light to collide eventually. In order to keep those protons in their circular orbits, the relativistic increase in their mass, a factor of 112, has to be taken into account to dynamically adjust the strength of the superconducting magnets according to their relativistic masses.
What did the teacher mean by ‘real’ here? That it is a measured effect and therefore true? In our ‘real’ experience, it is apparently the case that massive objects moving relative to us exhibit behavior that we cannot reconcile with the way we understand our daily reality. That is a reality that is made up of tangible massive objects that only deform when we exert forces on them. But those forces are not there in objects that move at constant speeds relative to each other. Don’t forget that those speeds are relative to each other. From Bob’s point of view he is at rest but from Alice’s point of view he moves at 100 km/h and his rulers are shorter than hers. In short, this is utterly incomprehensible if we want to maintain and understand the idea of an objective world outside us made up of massive material objects.
Reality as a mirror reflection of the Cosmic Mind
Relativistic effects, on the other hand, are very well to comprehend if we alter our perspective on reality by starting to understand our observations as projections of the content of the cosmic mind. Those observations are the reflections of the contents of a cosmic consciousness in the mirrors of our individual minds. That one great cosmic consciousness observes itself by its reflections in those myriad mirrors that living beings are. So, we are mirors of the contents of the cosmic mind. That reflected content behaves according to mathematical laws because the content of the cosmic consciousness is very probably the source of the mathematical laws Einstein found so admirable appropriate. This is by no means a new idea. Now may begin to understand why mathematics, a product of the mind, corresponds so well to observed reality. The math and reality we experience are both products of the mind*. The reality we see reflected in that mirror of our mind is a mathematical construction.
Material infinities, are they possible?
Also consider black holes. When the possibility of black holes was first suggested, that idea was rejected by most physicists. Their rejection was based on the fact that, according to general relativity, a black hole had to be a singular point, which is a mathematical infinity. A point without dimensions containing an enormous amount of mass. In a Newtonian universe made up of a countable number of material objects, material infinities cannot exist. Yet these days black holes are generally described and taken as actually existing. We even have a photo of it. But most people still live in a material reality made up of finite numbers of massive objects. Thats twisted thinking.
The measurement problem of quantum physics goes away
That the world is a projection or reflection of the contents of cosmic mind has also been proposed by me in my book as a solution to the measurement problem in quantum physics. The measurement problem is, in a nutshell, the idea in quantum physics that every object is a coherent* non-material probability wave, extending in principle everywhere in space, that ends abruptly in the material manifestation of the object the moment it is measured . How the measurement mamages this cannot be explained by a purely material view of the universe. But, in the idea that the world is a projection of the contents of the cosmic consciousness, perception has become almost identical to creation. Material existence is, like its observation, also a mind phenomenon. In your mind, rulers can shrink just fine and clocks will tick slower without any problem. Think about dreaming.
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.
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 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:
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:
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):
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.
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.
I do not belong to that part of humanity that believes that our brains produce our minds. Rather the reverse. If you study my website that should become obvious. As far as I am concerned, that is a well-considered position that has adequately dealt with my fear of death, the great nothing that lies ahead for all of us. So I no longer do have that fear. Which actually comes in handy with this corona crisis. From that perspective, your mind is not inside your brain, I have recently come across three interesting publications, a presentation on YouTube, a research report and a recent book that I would like to highlight here because they confirm and reinforce each other. This coming together of different scientific domains is called consilience.
Dr. Julie Beischel’s presentation at the SSE conference, June 2020
Dr. Julie Beischel is director of the Windbridge Research Center. She has PhD in Pharmacology and Toxicology with a minor in Microbiology and Immunology from the University of Arizona and has been studying controversial topics such as mediums with highly scientific methods for many years. She has subjected mediums, individuals who report experiencing communication with the deceased, to rigorous testing according to guidelines that every scientific research should always apply, such as double blind tests and the repeatable production of results. In addition, she also has a pleasant dose of dry humor as shown in her presentations.
In June 2019, Julie gave a presentation for the SSE on the subject of the identification we have with our body, which appears to be considerably more tenuous than we think. We part with it at the slightest occasion, as it turns out. In her presentation she discusses the ways in which we can easily lose that orientation, such as the rubber hand illusion, the speed with which our body renews, how much not-self-life lives in us such as our gut bacteria and the recent research by Etzel Cardeña from Lund University which presents very convincing evidence for the reality of PSI. Julie talks about striking (anecdotal) evidence from mediums that show that deceased relatives are still very concerned about their surviving descendants, about a verified and almost comical near-death experience, about a Thai boy who remembers a previous life as a snake who told in verified detail how that snake was killed. In short, you are not your body, it is a temporary avatar used by your real me, the real player, just like a self-chosen user image on websites or in video games.
View Julie Beischel’s presentation:
The Physical World as a Virtual Reality
Brian Whitworth published an interesting paper, The Physical World as a Virtual Reality, in 2007, where he puts excellent arguments forward for the idea that our world of experience is a Virtual Reality (VR). With the VR assumption, many properties of our experiential world can easily be explained that do not correspond very well with the usual assumption of a physical reality.
We view our world as an objective reality, but is it? The assumption that the physical world exists independently has been hard to reconcile for already some time with the goal of assimilating the findings of modern physics with the idea of an objective physical reality. Objective space and time should normally just ‘be’ there, but in our contemporary world, space shrinks and time slows down. Objective things should exist inherently, but in our world electrons are smeared probabilities spreading, tunneling, superimposing, and entangling in physically impossible ways. Cosmology now adds that our universe emerged from nowhere about 14 billion years ago. That is definitely not how an objective reality should behave!
In his paper he examines the possibility, one that is usually rejected out of hand, namely that the physical world is the result of a quantum process and thus virtual. What he proposes is not illogical, unscientific and certainly not incompatible with modern physics. Nor is it a modern idea because its origins date back thousands of years. His proposal is certainly relevant because modern physics has discovered that we actually live in a very strange world.
Consider the following counterintuitive but experimentally confirmed inferences from general relativity:
Gravity slows down time,
Gravity curves space,
Speed slows down time,
Speed increases the mass,
The speed of light is an absolute given.
And quantum physics also teaches us from her experiments:
Teleportation: quantum objects that ‘tunnel’ through a barrier,
Faster than light communication with entangled particles,
Creation out of nowhere,
Multiple existence of particles in different locations (two-slit experiment),
Physical effects without cause (radioactivity).
Whitworth argues convincingly that a VR not just explains excellently all these strange effects, but should even show them. A Big Bang can be explained for example as booting the VR program ‘Genesis’. Every VR program must have a beginning that, experienced from its inhabitants, seems to come from nowhere. The maximum speed that applies in our universe, on which Einstein based his theory of relativity but did not explain why there should be one, becomes the suddenly understandable consequence of the processor speed of the VR ‘computer’. In his proposal, a VR unites quantum physics and the theory of relativity, something where physicists still not have succeeded in after more than 100 years. At the end of his paper, Whitworth presents a very convincing comparison table comparing the properties that a VR must exhibit with the properties that we encounter in our ‘physical’ world. In other words, our bodies are Avatars. But who controls them?
Perry Marshall, computer programmer, businessman and internet marketer, writes Evolution 2.0. He is the opposite of an evolution biologist who wants to explain everything that lives and grows as coming altogether from purely accidenteel mutations, with the occasional favorable one that survives and transfers its properties to his posterity, combined with the Darwinian idea of survival of the best adapted (read mutated) specimen in the population.
Marshall views living organisms, such as the cell, from the programmer’s point of view. He concludes that DNA is code, not a random set of instructions, but a real code that is decoded, executed and if necessary rewritten, by the cell.
He argues using a lot of factual material and applying Claude Shannon’s information theory that DNA code cannot possibly have been created by chance. Coincidence generates noise and noise destroys information. Always and irreparable.
The possibility that the code of DNA plus the reading and decoding mechanism in the cell is generated by random mutations is astronomically small and would be an example of spontaneously decreasing entropy. Something we never perceive.
He says this: if you come across a code that is also interpreted and executed, you need a coder. According to him, that’s the cell. Or the intelligence that controls the cell. For him, the cell is an extremely complex and highly intelligent living being that actively and purposefully adapts to its environment by adapting its DNA. Mutations in the DNA are therefore no coincidences but adaptations of the cell in its DNA in an attempt to withstand the challenges of the environment. He provides an enormous amount of convincing experimental and published evidence for his claim. But then I’m going to wonder where the intelligence that the cell displays resides.
Consilience: Avatars, the world as VR and goal oriented adapting living cells
When I combine those three divergent matters together, the result is to me a fairly complete and logically coinciding picture of reality as we experience it in everyday life. Supported by these three pillars, PSI research, the physical properties that a VR must exhibit and experimental research on heredity, an image emerges of a world that takes place within a highly advanced computer game in which living things serve as avatars for something that is best described as a conscious mind. A game with the aim of development – ie evolution 2.0 – by a continuously challenging environment.
Challenging indeed, but but also with ample provision for fun and beauty would we allow each other the opportunity. Death is only the end of the avatar, not the controller. When the controllers goal has not yet been reached, he just chooses another avatar, which is reincarnation. And what does almost every near-death experiencer, who had left the game stepping back into it because his goal had not yet been reached, tell us? It was mainly about love, selfless love for the other. Without any exception.
During a course of mine on light & time, a student asked me during the break an excellent question to which I did not have a satisfactory answer in my own opinion at that moment. The student seemed satisfied, but the question kept buzzing around in my mind like a pesky fly in the room that couldn’t find the exit.
The Cosmic Microwave Background Temperature
Before I start to describe the question, let me say the following. It is my strong opinion that we can imagine an expanding EM wave as a cloud of photons expanding at the speed of light from the light source whose density decreases with distance from the source squared. But the energy per photon, I say, does not decrease with distance as the energy of each individual photon is determined by its frequency. Viewed in this way, Maxwell’s EM wave is a phenomenon emerging from the behavior of this photonic quantum cloud. It is a cloud of photons materializing according to their quantum probability waves , not the electromagnetic wave that is usually used to explain the wave behavior of light. For more explanation, see elsewhere on my website under ‘What is light?‘.
The student question was in response to my statement that the energy of a photon does not change with traveled distance because it would mean that its frequency would have to change accordingly. The universe background radiation, discovered in 1964 by Penzias and Wilson, with a wavelength of 7.35 cm and a temperature of 2.7 K, is today seen as a residue of the original radiation from the Big Bang. Due to the expansion of the universe, the original energy of the photons has decreased enormously. That the energy of the Big Bang photons has obviously decreased, contradicts my above statement that with the expansion of the EM wave, the energy of the individual photons does not decrease. So a very good question.
The redshift and the expanding universe
We encounter the same problem with the so-called redshift of light from galaxies moving away from us at great speed. The photons we receive from it here have gotten a lower frequency because of the so-called Doppler effect and that’s how Edwin Hubble discovered that the universe seemed to be expanding, as the light from galaxies showed a greater redshift on average the further away they were.
The Doppler effect stretches the wave
As a physicist, I like to approach such a question with a thought experiment that contains the basic ingredients of the question. Think therefore of a rocket whizzing away from you at half the speed of light. From the rocket a beam of light, i.e. photons, is sent back by a laser to be received by you. The laser emits violet light of a wavelength of 400 nm (750 Thz). When the laser has sent 1 wave, that’s 1 wavelength of course, then the wave must stretch, the wavelength as received by you becomes longer. The end of the wave is emitted when the rocket has covered half a wavelength since emitting the beginning of the wave because it’s going with half light speed. It must have covered a distance of 200 nm between these two moments . The wavelength, received by you, thus becomes 600 nm (yellow-orange). That indeed means that the photon you receive must correspond to a wavelength that is increased by af factor 1.5. The corresponding frequency of the foton becomes 2/3 of the emitted frequency – 500 Thz. The energy of a photon is directly proportional to its frequency (Planck’s law). The photon that you receive has therefore only 2/3 of the energy of the photon that was emitted. Energy is missing! Where does that energy go then? Isn’t that contrary to energy conservation?
The effect of relativity on the Doppler effect
Above that, we should not forget relativistic effects. If we choose to view the source, the rocket, as static and the receiver speeding away at half the speed of light, the outcome of the above Doppler calculation will be different. But because the speed of light is the same for all moving systems, we have to take that into account as well. We have to look therefore at the behavior of the clocks. You will ‘see’ the clock In the flying rocket ticking slower, because of the time dilation. The formula for that time dilation is: T=T0√(1 – v2/c2) where T represents the time in the rocket as seen by the stationary observer, you, and T0 the time for the stationary observer himself, so your own time. The ratio v/c=1/2, which gives in the time dilation formula: T = 0.866 x T0.
So in the time that 1 second elapses for you, 0.866 second elapses in the rocket. Not only the clock in the rocket will tick slower from your point of view, the laser will also be slowed in the same way and will emit light of 400/0.866 nm = 462 nm (indigo), from your point of view . The already lower energy of the photon received by you, due to the Doppler effect described above, is therefore extra reduced by an additional factor of 0.866. The wavelength of each photon that you will receive is thus, now including both Doppler effect and relativity, λ = (400 x 3/2)/ 0.866 = 693 nm (red). You will obtain the same result when you switch roles and assume a moving receiver (yourself) and a stationary source (the rocket). For a comprehensive explanation of the relativistic Doppler effect, see Wikipedia.
Energy conservation law and relativistic effects
Now the question is whether this relativistic decrease in frequency also violates energy conservation. But a closer inspection reveals that no energy is lost by relativistic effects. The relativistic decrease in frequency is the result of the slower time in the rocket as ‘seen’ by you as a stationary observer, so that less energy is sent to you per unit of your time. From your point of view, an ‘outstrechted’ photon of 462 nm (649 Thz) is emitted and also received (if we forget the doppler effect for a moment). The fact that this is experienced differently in the rocket, 400 nm (750 Thz), is only a consequence of the fact that the slowing down of the clock in the rocket is not experienced, since everything runs slower there in the same way. So the photon does not lose energy along its way to you due to the relativistic effect.
So back to the energy of the individual photon that seems to leak away through the non-relativistic Doppler effect. My first guess tells me that energy is not an absolute given in systems that move at different speeds relative to each other. Two bullets rushing next to each other at the same speed have no kinetic energy relative to each other, but they do have kinetic energy relative to their target. The same kind of thinking could therefore probably apply to photons. We should search for a solution in that direction.
Is a photon a closed system in terms of energy conservation?
After thinking about the question for a some time, I did come to the following conclusion. Conservation of energy only applies to closed systems. Apparently a photon cannot be considered as a closed system, even not as a system in the usual sense. That image of a closed system seems to come from considering the photon as a real particle speeding through space. But in my opinion a photon is really nothing more than the our material interpretation of an event in which an energy exchange takes place between two systems. As long as those systems do not move relative to each other, the energy change in one system will be equal and opposite to the energy change in the other. The registration of received energy is what we interpret as the flight of the photon. It seems to us as if there is a flying photon carrying energy over, but there is no particle flying through space. It is our interpretation of an amount of energy that disappears from its source to appear elsewhere. Should such a non-existing particle be regarded as a closed system in which the total energy remains the same?
I assume it has to do with the fact that in order for the photon to arrive at me apparently at the speed of light, it has to compensate for the speed at which the rocket speeds away from me. And this compensation costs energy. Compare it with shooting a bullet from a speeding train to a target standing next to the railway track. The kinetic energy of the bullet that it received from the gun is not equal to the kinetic energy with which it hits the target. That’s less in the case the train speeds away from the target. Part of the kinetic energy of the bullet is then spent on the difference in speed between the train and the target. But this is not in contradiction with the preservation of energy. I hope you can understand that. The bullet is not losing energy on its way to the target, provided that air resistance can be ignored.
As soon as the two systems move relative to each other, an imbalance in energy exchange exists. It takes extra energy to send energy to a system moving away from you. But this extra energy is not added to the photon. So for energy conservation you have to look at the total system, photon, sender and receiver, not only at the photon. The greater the speed difference between the systems, the greater the imbalance between spent and received energy. And that explains the low energy of the cosmic microwave background radiation. Its source, the remains of the Big Bang explosion, is moving away from us with a speed which must be very close to the speed of light. Very little energy is left for the photons coming our way. They do not lose their energy on the way. From our perspective they started 13.7 billion years ago with that small amount of energy because most energy was spent on compensating for the speed with which their source was receding from us.
Conclusion: the imaginairy existence of the photon
Considering the photon as a material traveling particle that carries and transfers a specific amount of energy through space leads to these kinds of difficult contradictions. Elsewhere on this website I’ve argued that the photon, while most of the time a useful, however abstract, concept, doesn’t exist along the way and is probably completely imaginary. There is energy that disappears in one system and energy that appears in another. Something in which the quantum state wave plays a major role. And between disappearing and appearing there is a time difference that, divided by the distance between the systems, always turns out to lead to the observation of the speed of light.
My statement that the EM wave is the result of a cloud of photons expanding with the speed of light, whose energy per individual photon does not decrease, must therefore be extended with the condition that the source does not move relative to the observer. No problem at all.
Quantum physics is at the moment not yet a theory, argues Tim Maudlin, because quantum mechanics is still just a recipe, a formalism, that offers no ontological view of the world. I fully agree.
Gerard ’t Hooft still hopes for a theory describing an objective reality that would be based on information.
Roger Penrose hopes to find the solution for quantum physics and consciousness in the interaction between the microtubules in our neurons, gravity and consciousness.
Chiara Marletto mainly points out the incompatibility between the ‘sharp’ theory of relativity and the ‘blurry’ quantum world but does not offer a way out.
Philip Ball wholeheartedly acknowledges non-locality, the absence of properties of the quantum object until the object is measured, but offers us only words with no ontological comfort, so that we should just content ourselves with the weirdness for it to go away.
Watch this movie “Living in a quantum world” from Vlatko Vedral on YouTube: https://youtu.be/vaUfZak8Ug4. At the end of his presentation a question from the audience about time and quantum physics is asked (at about 1: 10) and in his answer he describes the behavior of a super-accurate clock and what happens to the last digits when you lift that clock half a meter in the gravitational field. And then he wonders what it means when you imagine that clock to be in a quantum superposition at the two different heights in the gravitational field. A superposition of two different timelines. Fascinating.
By the way, the first part of his presentation – about 45 minutes – is actually a very compact version of my quantum physics book. Everything is presented in an almost blazing speed: interference, the Mach-Zehnder interferometer, Schrödinger’s cat, the Copenhagen interpretation against the multiverse interpretation, delayed choice experiments, interference with very large molecules shot through double slits, the orientation of our robin on the earth’s magnetic field in its annual migration, the 100% efficiency of chlorophyll. Highly recommended.
Quanta Magazine, a web service which often brings interesting articles, published shortly an interesting article where relativity, quantum physics and black holes played an important role. However, in reading it I did hit upon a very common misconception, about which I like to comment here.
Quote from: Einstein, Symmetry and the Future of Physics | Quanta Magazine
“Solar energy arrives on Earth and becomes mass in the form of green leaves, creating food we can eat and use as fuel for thought. “
The misconception is that mass and energy are different things and that energy is somehow mysteriously converted into mass and vice versa. However, that’s not the message of E=mc2. Energy and mass are, in the opinion of almost all physicists, more like the two sides of the same coin. They are identical. This can be understood by considering what happens when an object is accelerated up to the speed of light.
According to the special relativity, all the energy that you spend into that acceleration is converted into inertial mass. It will cost you more and more energy to keep accelerating it. That is why we can never reach the speed of light itself in this way, the inertial mass would become infinite. This effect has been convincingly demonstrated when accelerating protons in the Large Hadron Collider at CERN. The faster they go, the more mass they get and the stronger the magnetic fields must be to keep them neatly in their circulair loop.
In general relativity, the central basic assumption is that inertial mass and heavy mass are identical or that the acceleration force due to gravity is identical to the acceleration force that you encounter in, for example, a merry-go-round. The implication therefore is that inertial mass, heavy mass and energy are really all the same fundamental thing. This means for instance that a charged battery must also be slightly heavier than when discharged. However, the energy released by nuclear fusion is often explained in popular terms as follows:
“The mass of the two fused atomic nuclei is smaller than that of the original fused nuclei together. That mass deficit has become energy and that mass is gone.“
Thus it seems as if mass alone is not conserved, mass plus energy should be the conserved property. However, Wikipedia says otherwise: “Mass and energy can be seen as two names (and two measurement units) for the same underlying, conserved physical quantity. Thus, the laws of conservation of energy and conservation of (total) mass are equivalent and both hold true”.
Ponder this. The fused atomic nucleus has received an enormous amount of kinetic energy during the fusion, and that is speed. That kinetic energy is exactly having the same mass as the ‘disappeared’ mass. So, that mass has not disappeared at all. Due to the speed with which the fused core now moves, which means kinetic energy, it also has more mass. That is the message of special relativity. If you could have this fusion taking place in a thermally completely sealed box balanced on a pair of scales, you would find zero difference in weight – and therefore in mass.
Another but related topic. That every observer always observes the same speed of light is a physical observation but goes against our so-called common sense which tells us how adding up speeds normally works. Elsewhere on this website I say something about that in ‘What is light‘.