Saturday, August 01, 2020

What is the equivalence principle?

Folks, I recently read the website of the Flat Earth Society. I’m serious! It’s a most remarkable collection of… nonsense. Maybe most remarkable is how it throws together physical facts that are correct – but then gets their consequences completely wrong! This is most evident when it comes to flat earthers’ elaborations on Einstein’s equivalence principle.

The equivalence principle is experimentally extremely well-confirmed, yes. But flat earthers misconstrue evidence for the equivalence principle as “evidence for universal acceleration” or what they call the “universal accelerator”. By this they mean that the gravitational acceleration is the same everywhere on earth. It is not. But, you see, they believe that on their flat earth, there is no gravity. Instead, the flat earth is accelerating upwards. So, if you drop an apple, it’s not that gravity is pulling it down, it’s that the earth comes up and hits the apple.

The interesting thing is now that flat earthers’ claim Einstein said you cannot distinguish upward acceleration from downward gravity. That’s the equivalence principle, supposedly. So, you see, Einstein said it and therefore the earth is flat.

You can read on their website:
“Why does the physics of gravity behave exactly as if the earth were accelerating upwards? The Universal Accelerator answers this long-standing mystery, which has baffled generations of scientists, by positing that the earth is accelerating upwards.”

Ingenious! Why didn’t Einstein think of this? Well, because it’s wrong. And in this video, I will explain why it’s wrong. So, what is the equivalence principle? The equivalence principle says that:
“Acceleration in a flat space-time is locally indistinguishable from gravity.”
Okay, that sounds somewhat technical, so let us go through this step by step. I assume you know what acceleration is because otherwise you would not be watching a physics channel. Flat space-time means you are dealing with special relativity. So, you have combined space and time, as Einstein told us to do, but they are not curved; they’re flat, like a sheet of paper. “Locally” means in a small region. So, the equivalence principle says: If you can only make measurements in a small region around you, then you cannot tell acceleration apart from gravity. You can only tell them apart if you can make measurements over a large enough distances.

This is what Einstein’s thought experiment with the elevator was all about. I talked about this in an earlier video. If you’re in the elevator, you don’t know whether the elevator is sitting on the surface of a planet and gravity is pulling down, or if the elevator is accelerating upward.

The historical relevance of the equivalence principle is that it allowed Einstein to make the step from special relativity to general relativity. This worked because he already knew how to describe acceleration in flat space – you can do that with special relativity. In general relativity then, space-time is curved, but locally it is flat. So you can use special relativity locally and get general relativity. The equivalence principle connects both – that was Einstein’s great insight.

So, the equivalence principle says that you cannot tell gravity from acceleration in a small region. That sounds indeed very much like what flat earthers say. But here’s the important point: How large the region needs to be to tell apart gravity from acceleration depends on how precisely you can measure and how far you are willing to walk. If you cannot measure very precisely, you may have to climb on a mountain top. You then find that the acceleration up there is smaller than at sea level. Why? Because the gravitational force decreases with the distance to the center of the earth. That’s Newton’s 1/R2 force. Indeed, since the earth is not exactly a sphere, the acceleration also differs somewhat between the equator and the poles. This can and has been measured to great precision.

Yeah, we’ve know all this for some while. If the acceleration we normally assign to gravity was the same everywhere on earth, that would contradict a huge number of measurements. Evidence strongly speaks against it. If you measure very precisely, you can even find evidence for the non-universality of the gravitational pull in the laboratory. Mountains themselves, for example, have a non-negligible gravitational pull. This can, and has been measured, already in the 18th century. The gravitational acceleration caused by the ground underneath your feet has also local variations at constant altitude just because in some places the density of the ground is higher than in others.

So, explaining gravity as a universal acceleration is in conflict with a lot of evidence. But can you instead just give the flat earth a gravitational pull? No, that does not fit with evidence either. Because for a disk the gravitational acceleration does not drop with 1/R2. It falls more slowly with the distance from the disk. Exactly how depends on how far you are from the edge of the disk. In any case, it’s clearly wrong.

The equivalence principle is sometimes stated differently than I put it, namely as the equality of inertial and gravitational mass. Physicists don’t particularly like this way of formulating the equivalence principle because it’s not only mass that gravitates. All kinds of energy densities and momentum flow and pressure and so on also gravitate. So, strictly speaking it’s not correct to merely say inertial mass equals gravitational mass.

But in the special case when you are looking at a slowly moving point particle with a mass that is very small compared to earth, then the equality of inertial and gravitational mass is a good way to think of the equivalence principle. If you use the approximation of Newtonian gravity, then you would describe this by saying that F equals m_i times a, with m_i the inertial mass and a the acceleration, and that must be balanced with the gravitational force that is m_g, the gravitational mass of the particle, times the mass of earth divided by R^2, where R is the distance from the center of earth which is, excuse me, a sphere. So, if the inertial mass is equal to the gravitational mass of the particle, then these masses cancel out. If you calculate the path on which the particle moves, it will therefore not depend on the mass.

In general relativity, the equivalence of inertial and gravitational mass for a point particle has a very simple interpretation. Remember that, in general relativity, gravity is not a force. Gravity is really caused by the curvature of space-time. In this curved space-time a point particle just takes the path of the longest possible proper time between two places. This is an entirely geometrical requirement and does not depend on the mass of the particle.

Let me add that physicists use a few subtle distinctions of equivalence principles, in particular for quantum objects. If you want to know the technical details, please check the information below the video for a reference.

In summary, if you encounter a flat earther who wants to impress you with going on about the equivalence principle, all you need to know is that the equivalence principle is not evidence for universal acceleration. This is most definitely not what Einstein said.

If this video left you wishing you understood Einstein’s work better, I suggest you have a look at Brilliant dot org, who have been sponsoring this video. Brilliant offers online courses on a large variety of topics in mathematics and science, including physics. They have interactive courses on special relativity, general relativity, and even gravitational physics, where they explore the equivalence principle specifically. Brilliant is a great starting point to really understand how Einstein’s theories work and also test your understanding along the way.

To support this channel and learn more about Brilliant, go to, and sign up for free. The first two-hundred people who go to that link will get twenty percent off the annual Premium subscription.

Thanks for watching, see you next week.


  1. So... not only is it turtles all the way down, but the turtles procreate quickly enough to generate one gravity of acceleration?

  2. Hi Sabine,
    You wonder why the FlatEarthers have so many facts wrong and nevertheless make the wrong conclusions. I think the explanation is simple: they do not start from the facts to arrive at conclusions, but they take the opposite direction: they start from conclusions and thereafter look for facts which can be interpreted as to support the conclusions. And some will even use ‘alternative facts’ if needed. In case of FlatEarthers this is not very noxious and one can just be amused with their opinions. Unfortunately in the present time period we see the same behavior with people who can do much more harm to our society. But this too shall pass. Although emotions are far more powerful than reason In determining human behaviour, reason has truth on its side.

  3. There needs to be a line feed/carriage return between “upwards.” and “Ingenious”, otherwise it looks like your statement is part of the quote from the website

    1. Rick,

      Thanks for spotting this; I have fixed it. (Carriage return! Haven't heard that for ages!)

  4. I have not personally come face to face with a flat-earther. I do know someone who has, and in fact she has a flat-earther for a neighbor. I have not gotten into it with this flat-earth person, --- yet. This is a good explanation for why flat-earth ideas are nonsense, but of course this is mostly preaching to the choir. Maybe indirectly others watching this can carry the torch to those less enlightened.

    I have suggested one way to induce cognitive dissonance in a flat-earthers. This is with the moon. The moon moving around just below this dome would appear larger at different places as it would be closer to the edge. It would in addition have a different limb appearance as line of sight would be different at various geographic locations. Also, if they propose the moon is a flat disk on this dome, then it would tend to appear more as an ellipse to people looking up where the dome is curving down. In both of these cases the inclination and declination of the moon would have a different dependency than known. You can I think have lots of fun with this, though I have not tried it yet. I have yet to meet a flat-earther face to face, or at least where I know they are a flat-earther. With the moon there is no need to appeal to any physics at all.

    I have been aware the flat Earth movement has been on the rise. I saw a news report about a convention on such, where various hustlers were selling models of the flat-earth world. I am not aware of this being as yet popular in Europe or Japan and the rest of the developed E. Asian region. There was a dare-devil idiot who flew a steam powered rocket a couple of km up with some intention of proving a flat Earth. His latest attempt failed, and he perished in this crashing to the ground.

    This is one reason the religious based creationist movement is pernicious. This has set up a mindset where science supposedly cannot be trusted. In the wake of there have come various popular ideas. One related to flat Earth is geocentrism, which has quite a following. At least they get the Earth’s surface as a sphere. There have been other things, from anti-vaxers, moon hoaxers to conspiracies of many sorts, including one about space-alien reptile men taking over the world. That last one is fun! There has been a general disintegration of the American mind, where a wide and growing range of nonsenses are cementing themselves in people’s minds. There is also an industry of media disinformation that is shameful.

    I read this morning that 50% of Americans are refusing to be vaccinated against Covid-19 when the vaccination comes out. I also read a pro-med report that immune globulin against CovSARS-2 is mostly absent in titers from people 90 days after contracting this. So, I have some doubts on the efficacy of a vaccine. However, anti-vaxers see this as a conspiracy, with ideas of putting computer chips into people and so forth. There is a proposal to use quantum dots in poor regions to tell if people have had the vaccine. The refusal and denial of science, which has impacted environment and climate issue to now health and pandemic concerns is a disaster. That the United States has many times the number of infections and deaths, and per capita as well, is I think a direct result of this sort of rubbish thinking.

    Now an update on my aftermath with Covid-19. Folks, you really, really do not want to get this. The after-effects of this have turned into a big problem. I can go into this later. I feel I have aged 5 or 10 years, have fatigue, joint pain (never had that just a few months ago) and there is a sense that neural or brain apps or circuitry has been changed. Mask up and do the right thing!

    1. Lawrence: Sympathies on your Covid-19 aftermath.

      I think the general disintegration of the American mind is more like a reversion; another effect of the Information Age.

      People don't trust science. In part because people in power (politicians and corporations) attack it when the results of science are unpopular or suggest we should stop doing something popular or profitable.

      In part because science itself has fallen victim to the profitable hype paradigm, making promises (or what seem like promises) to the masses, often to secure funding or more funding, and then failing to deliver.

      How many dozens of "this could be a cure for cancer" have I seen in the last four decades? I've lost count.

      our FDA doesn't do its job; or is prohibited from doing a proper job. Huckster "cures" for everything are rampant, allowed to be sold as unregulated "nutritional supplements" with suggestively worded marketing.

      Schools have joined in; educational standards keep finding new floors to fall through. In the current Covid-19 crisis, we have revealed their true utility -- they have devolved into daycare centers for kids 5-18. That's why Trump is so insistent they must reopen, no matter how many teachers die, because the economy needs all those workers freed up by daycare.

      The American people do not trust science, or medicine with good reason. Both are grievously infected by the Big Bucks virus and do not deserve to be trusted. Thanks to the Information Age (which I think is good) Religion is not much better, with revelations of pedophilia and cover ups. Politicians are no good, with revelations of corruption and getting away with blatant law-breaking, on both sides of the aisle.

      As far as Science is concerned, where are the breakthroughs they keep promising? What ever happened with that LHC, besides building an impressive machine and wasting money?

      Where's that cure for cancer, and Alzheimers, and what the hell is going on with Autism?

      The American Mind (and I am sure many others) is reverting to the evolutionary standard of Tribalism. The Enlightenment is over.

      If you cannot trust the authority of Government, Academia, Doctors, Scientists, Political Parties, Corporations or the Church, where do you turn?

      For the vast majority of people that are not critical thinkers, the answer is to pick one they want to be true, and latch on, and ignore or fight the others.

      That's the future. We have failed to apply science to the management of governments, corporations, health-care, doctors, medicine and pharmaceuticals, academics and charities in a way that minimizes corruption, self-service, and autocratic powers.

      Autocratic powers are rampant in America, including the district attorneys that can choose to not prosecute murderers, the immunity of police, to judges, Mayors, Governors and Presidents. The Leaders of the House and Senate have pocket veto power. On the business side, autocracy is the nearly undisputed rule. Within the Military, the same thing.

      This is the result, tribalism. Everybody outside your chosen tribe is trying to con you. If we deny the dogma of your tribe, we'd best find another one.

      Welcome to the Information Age. For some it can be Enlightening. For most it is Endarkening. Everything is hype, nothing can be trusted. They are not critical or logical thinkers, so they just have to pick a tribe and hope for the best.


    2. Lawrence, may you be truly well again soon.

      Dr. A.M., you give an excellent outline of our difficulties, and of our limitations in coping with them. These are compounded in loving families such as mine, where we have different views. Your 'Information age hype' makes it beyond difficult to find well-documented references in trying to bound these differences.

    3. There is a limit to this. People are not reading as much these days. Reading skills are declining. What will happen in the future when we have an extremely advanced technical society and ever fewer people are able to read and study well enough to understand it?

      The result of this is as you point out contrary to the promise of the information age. I am not a panegyric of censorship, so any idea for some net-censors who remove bad or erroneous nonsense risks an out of control censorship that could squelch anything. Also, take my word for it; bible thumpers will work to be the big censors if they can.

      The US is poised to lose its position in the world. It may take a while longer, but the populace is largely not up to being sharp focused. We also have lots of social dysfunctions here. Students at science departments are mostly from Asia and China, and this points to where the center of gravity of science and intellectual progress will shift in the coming decades.

      American students are much more MAGA hat wearing types studying business administration. I am somewhat real about that observation. Welcome to the endarkenment.

    4. Dr. Crowell, thanks for your thoughts and warnings about COVID-19. I have seen news reports of several studies and other personal testimonies about the aftermath of COVID-19, including heart damage. As to the lack of antibodies, there is a hypothesis with I think some data behind it that the immune system has some sort of memory cability so it does not have to keep producing antibodies to all the diseases and vaccinations it has had long after the occurrences but can respond quickly to re-occurrences. That may be wishful thinking and also COVID-19 might be a rapid-mutater like the flu, however. I guess we will find out after an effective vaccine is available and widely used.

      Meanwhile, the next time somebody encourages me to be less cautious (I wear a mask even to go for a short walk and have stopped going to restaurants or meals in other homes) I will email your last paragraph to them (along with some other data). (If I have their email address.)

      A good novel to read, in my opinion, while semi-self-quarantining, is Neal Stephenson's "Anathem". I finished it for about the third time recently. It discusses, in fictional form, some of the ideas that have been debated here, and I found myself envisioning some of the more prominent commenters here as some of the characters. It is science-fiction, but of the more thoughtful sort that explores societies and concepts different than the ones we currently have. Plus I enjoyed the characters and plot.

    5. @lawrence:

      I do hope you recover fully from Covid-19.

      I just read in our local paper of a story about a USA citizen who was so convinced that Covid-19 is a hoax that he held a party at a restaurant where no-one wore face masks. Apparently quite a few caught the virus and several died, including his mother. Of course now he's recanted his earlier disbelief. It's a shame that for some people this is what it takes.

      Personally I don't think that we've as a society have become less literate, but that that as a society, the written word doesn't hold the place it once did. There are now other modes of communication - audio and video and they are much more prominent. It does mean that news and media has suffered as result.

      I've heard a lot recently about how the centre of gravity of science and tech are shifting East. But a society like China had a lot of catching up to do, so much of it is new to them. Similar to Japan in the late 19th C. Recently I read in Physics World that Japan was also complaining about a fall off in science recruitment. So it seems more of a problem with mature industrialised and technological societies than something that is Western.

    6. The Covid-19 issue is a clear case of the pernicious impact pseudoscience has. It is strange to think disinformation on the nature of the Earth in space or denial of the evolution of organisms can have an impact on health. Even further, this sort of anti-science ideology has a clear connection with the current social hypermanic movement.

      I read a couple of weeks ago a Pro-Med on how immuno-globulins for CovSARS-2 were either mostly reduced or absent in titers of patients who recovered after 90 days. The common cold is a corona virus and similarly our immunities to it are temporary. This is potentially a huge problem. The big goal is a vaccine, but how effective can a vaccine be if immunity is largely gone in 90 day? Even if we get a vaccine it could be that we may have to keep getting it every 90 days. Believe me, if a vaccine is developed, I will get it every 90 days if needed.

      The other much larger problem is this means many will be getting this illness several times a year. The virus is an angiotensin-converting enzyme 2 (ACE-2) receptor, which is abundant in the epithelial tissue of organs and inside arteries. The common cold is an ACE-I receptor that is in the throat and trachea. The CovSARS-2 could then repeatedly infect people and cause accumulated damage to this tissue. It points to the prospect for an upsurge in congestive heart failure, kidney and renal disease, COPD type lung problems and so forth. In the next 5 years we may have a pandemic of these types of disorders and a dropping life expectancy.

      For people who think the pandemic is a hoax I advise them to call a funeral home to ask how their business is going.

      Ecology functions to amplify negative feedbacks on a species that is overpopulated or abundant. A plant species that is over-abundant is often subject to fungal infections. Animals often die in large numbers by bacterial or viral infections. We are no different, and as we tear up natural ecosystems, we put ourselves or our crops and livestock at increased risk for exposure to unknown bacteria and viruses. We have in recent decades seen the appearance of new diseases, the worst being HIV, Ebola and now Covid. Brace yourselves, we will probably see more of this. I do not see any reduction of eco-destruction of rain forests and other ecosystems and human populations continue to grow and press into these regions. This is a good time for opportunistic microbes or wannabe parasites.

  5. If I am not wrong what is presented above has to do with the weak part of the equivalence principle (see Einstein's Elevator thought experiment).

    Furthermore, there is the strong equivalence principle where the gravitational mass of a body is equal to its inertial one. The interesting thing here is there are many experiments searching for violation of the strong principle and one of them is the searching for the Nordtvedt effect (a very exciting field of research).

    In case the Nordtvedt effect really exists then it will prove that objects falling into a gravitation field will fall at different speeds depended by their gravitational self-energy and not because of their mass. In other words it will prove what Aristotle said some 2400 years ago, "Heavier objects fall faster".

    Since we are still on the thought experiments tracks, I think the violation of strong equivalence should be already demonstrable with a mechanical device (Proof of concept in macro-world) under the influence of earth's gravitational field. IF the test is proved to be successful then later one may create (it is very easy) a special quasiparticle (quantum-mechanics equivalent of the mechanical construction) under the influence of earth's gravitational field.

    It seems the violation of the strong equivalence principle goes hand in hand with the breaking of action-reaction symmetry (see my Profile). Solid bodies (no internal structure) or bare particles will never show a Nordtvedt effect because there is no way to influence solid body or bare particle gravitational self-energy.

    And for those who are not aware about it, I will say that the breaking of action-reaction symmetry has been already experimentally confirmed in other disciplines of physics as Optics, Statistical mechanics, Condensed matter etc.

    The question that arises for me is: Since the breaking of action-reaction has been already experimentally verified and assuming (according to me) that is related to the violation of the strong equivalence principle then why the Nordtvedt effect is still not detected?

    The answer can be found on a comment I posted in the previous subject of this blog (..Thought Experiments) and is more or less the following: "Modern physics has discarded logic in favor of abstract maths that essentially lead to results that have nothing to do with reality.".

    In other words, consistency in a theory enables the creation of suitable experimental setups in order to detect what you are searching for, otherwise the experimental results will always be
    null (see Nordtvedt effect, Eötvös experiment results etc).

    1. John, as pointed out in reply to the previous comment you mention, hypothetical proof is not the same as proof. Neither does stating that action-reaction has been disproved disprove it. As you say, the Nordtvedt effect has not been shown to exist. To me, the answer to your question is probably "because it doesn't".
      Sorry, (and after all I interpret your work from the POV of a very old engineer. 😎)

    2. This has been tested with multiple neutron and dwarf star systems. The Nordvedt effect has for instance the Earth gravitating differently with the sun than does not moon. The gravitationa self-energy is presumed to cause a deviation in their motions. However, several neutron star systems have been examined and the strong EP has been found to hold to 2.6×10^{−6}. The gravitational pull of a triple star system PSR J0337+1715 consisting to two white dwarf stars and a neutron star has lead to these results [ arXiv:2004.07187 ]. The neutron star in a tight orbit with one of the white dwarfs is perturbed by the second in a more distant orbit with lower frequency. This is a null result ib the Nordvedt effect and the strong EP so far holds.

    3. @Korean,
      I don't think you pay attention to what I wrote above or in general but this is not my problem. One has first to read what I shared through my Profile then, search what are the References all about and only then one should normally express his/her own point of view. Of course, I can be also wrong but then and only then we could have a real conversation about that subject. Otherwise, your comments has no worth and do not address my arguments. The Nordtvedt effect will never be detected when we search this effect around solid bodies e.g. particles, neutron start etc

      As I mentioned above the strong EP will always hold as long as we are doing experiments with solid bodies (no internal structure). I insist the strong EP can be demonstrated with a classical mechanical device and on quantum level using a special quasiparticle.

      How to violate (John's thought experiment) strong EP on quantum level:
      1.Trap charged particle/s within a standing wave -> charged particle and standing wave become a system that resembles a quasiparticle
      2.Place (1) along the lines of earth's gravitational field
      3.Let (1) being influenced (free fall) by earth's gravitational field
      4.Because of general relativity there will be a blue shift (similar to Pound-Rebka Experiment)
      5.Force (1) to apply a phase shift to the standing wave that is equal but in opposite direction to (4)
      6.(5) just cancelled the gravitational blue shift

      Even by ignoring of what I just proposed above, Pound and Rebka had already shown the way but as I have to repeat for once more "Modern Physics has discarded logic in favor of abstract maths that have nothing to do with reality". In Pound-Rebka experiment is according to my opinion hidden the key to quantum gravity.

      In other words, (6) and generally quasiparticles are the only entities that may violate strong EP. What happened above is the quasiparticle (standing wave + particle) counteracted the external gravitational field by reducing its own energy. As phenomenon it will appear floating and not falling into earth's gravitational field.

      It means also that none of the current running experiments (any kind of experiment in this direction) will ever (even by waiting for another 13.6 billion of years) detect a violation of strong EP because they are running a wrong setup (solid bodies as netron stars or bare particles as electrons etc).

    4. [I'm jot sure whether this posted. Please delete if this is a duplicate. Thanks]


      I know that modern abstract maths gets something of a kicking sometimes. Nevertheless, it has actually achieved a great deal - despite itself - or maybe because of itself.

      For example, I never particularly found tensors as explained transformationally as in traditional physics texts at all intuitive. Which was really annoying and irritating as I really wanted to get to grips with GR. So this was quite a stumbling block for me. Personally, I think I'd been spoilt by vectors which have an immediacy which tensors don't. But perhaps I was expecting too much. After all, Newton did without them. They had yo be invented and then promoted as Heaviside & Gibbs did so ably.

      But shouldn't there be something similar for tensors?

      Well, mathematicians have come up with a way of explaining them geometrically that makes much more sense and it's a real pity that this is not more widely known.

      Another example are vertex algebras. These arose from CFTs like the worldsheet theory of a string or in some condensed matter systems at a critical point. Again they don't look intuitive especially the locality axiom but Costello & Gwilliams factorisation algebras have a natural interpretation in QM, especially the locality axiom and vertex algebras can be explained in terms of them. Another way is via an operad which parametrise all the 3-point functions.

      A less esoteric example is calculus on manifolds which really all physicists should learn rather than the clumsy grad, div & curl we are used to. An added bonus is that the notions of a potential field and a conservative force field are placed in a more structurally meaningful way ie de Rham cohomology.

      This has pay-offs like saying the obstruction to classical observables being lifted to quantum observables in perturbative QFT through quantisation can be measured through the first cohomology group.

      Oscar Wilde said the USA and Britain were a common civilisation divided by language. Ditto the physics and maths world.

      For example, if took me a hell of a long time to learn what gauge fixing, gauging, local gauge, the gauge group, the gauge covariant derivative etc, etc were because of this Babel of languages...

    5. Further comments: The idea offered is that a standing wave on a gravitating body is a case for the violation of the EP. The quantized variant of a ball bouncing on the floor is a standing wave that has exact solution according to Airey functions. The “atmosphere” of a neutron star might have this physics. We might ponder quantum basketball with particles dribbled on the floor by driving forces and with processes that attenuate their energy. If we wrap the gravitating body into a sphere and keep it Newtonian the radial solution is given by Laguerre polynomials. If we let the gravitational field become relativistic then things do get decidedly more complicated.

      Why is this not a violation of the EP? The reason is there is a hard surface that stops the geodesic flow. A quantum wave that reflects off this surface is no longer on a geodesic. The accelerated version of the EP comes into play then. This is not a case of such a violation of the EP.

    6. @Mozibur,
      Well advanced maths like Tensors and stuff resembles me the todays chaos with the programming languages that means as abstract and more specialized the better because one does not need to take care the details since they are taken care by the framework of the programming language itself. That is all fine! What is the gain? The gain is we can solve complex problems with easy as also we may develop other ideas with easy. The only drawback now with the advanced maths is when one is interested to explore fundamental structures then due to the abstractness of the math, one may miss or take for granted some details (that are enclosed and hidden in the framework of math), something that may lead the researcher to paths that have nothing to do with reality.

      I am a little confused about your comment above, if your argument addresses the thought experiment I shared then, I don't think we are on the same page. I speak for real standing wave-particle system and not for what the Wave function assumes for a quantized variant when is mathematically solved as in your example.

      When we conduct both experiments (my thought experiment) and yours (with the necessary adjustments to meet the requirements of the setup), yours will fail. Why? Because the quantized variant of that thing is actually not trapped within a standing wave. This is where QM will be proved to be wrong (and especially the Wave Function itself). The Wave function as I have supported in older posts models the observation (past the interaction) by ignoring the mechanism of the effect itself. In other words, a quantum variant is not travelling with a standing wave as also is not a standing wave even the established tools (Wave Function is a mathematical tool, nothing to do with reality) and interpretation say so.

    7. If we are discussing the EP and particularly with the putative idea of Nordvedt that gravitational self-mass violates strong EP, then we are talking about freely falling frames. Nordvedt postulates the mass in the gravity side of ma = -GMm/r^2 is renormalized, while on the ma side it is not. This has been experimentally found not to hold, at least so far. As such this physics does not appear realistic and further it does not involve in principle a solid surfaced body, such as a black hole.

      As a correction of sorts to my comments above. I said if the flat surface were wrapped into a sphere the wave would be Laguerre polynomials. That would be approximately the case if the wavelength is much longer than the radius of the sphere. The case where the wave is comparable or shorter than the radius things get complicated and Laguerre functions are maybe approximate.

      This is a truncated version of a post I sent that did not appear. I had a link to Nature which might have been the problem.

      The idea of composite structures and quasiparticles is invoked. Those of us who did a thesis in gravity or particle physics tend to look down on solid state physics, and I have come through work to see this as unfortunate. We tend to think of elementary particles as somehow fundamental, while quasiparticles in a crystal are more epiphenomenological and less fundamental. To be honest, I see what we call fundamental particles are themselves quasiparticles. Experiments that demonstrate the quantum Cheshire Cat point to this. [website address to removed]

      We can see the two-slit experiment as a form of entanglement. We think of this as a superposition of states, and of course if we put a spin state as a detector in a slit the quantum phase of the wave is converted to an entanglement of the particle and the spin state. Yet even before we can think of the particle as in a region, a sort of black box if you will, moving to the slits, with the state |01〉 + |10〉 that is a type of Bell state. The same for the spin and charge of an electron. These are topological quantum numbers, and there is no reason to think an electron is an entanglement of these two quantum states. The spin would be up or down, and the charge is then is two possible states through a Stern-Gerlach apparatus or interferometer as being “here or there.”

      I am a bit uncertain about your claim that QM is wrong. Where quantum mechanics has trouble is that it is a closed system. We generally quantize some specified set of observables to have a well-defined number of degrees of freedom. Decoherence and measurement is a case where a quantum system is coupled to an open environment of states. In this setting a quantum system of interest communicates its quantum phase to some unspecified number of states. Classical mechanics pertains well to open systems. A classical system with N states, let us think of them as binary, has complexity 2^N. This is an estimate of the Kolmogorov complexity of a system of binary symbols in a classical or non-quantum system. For a quantum system of states complexity is exp(2^N), where for N large enough this is an enormous number. From the perspective of tractable calculation this is why QM is not good for open systems. This does not though mean QM is false.

    8. @Lawrence,
      Dont't worry about what I write above because I can be also wrong. I am not a physicist and certainly you know more than me regarding QM and general Physics. I am just an Engineer having my own understanding of how things work (it is a matter of interpretation or even stubbornness) based on my own observations and some physics/math knowledge I have.

      Since you refer the quasiparticles, I will say this: The future belongs to quasiparticles in all aspects of physics from supercomputing, fusion up to controllong gravity (more accurately controlling self-inertia/gravitation field). If I had to invest on a research, I would put my money on quasiparticles (whatever).

      The mechanical equivalent of a quasiparticle (a type e.g. is a travelling standing wave having trapped some matter within) is presented in Fig.2.Upper (see my Profile). This simple construction can be the key to many mysteries (as the thought experiment I presented above and especially regarding quantum gravity) in Physics.

    9. A quasiparticle is some physical effect of a crystal lattice that in quantization assumes properties similar to a particle. The classic example is the phonon. A lattice vibration that is longitudinal is the quantization of acoustical waves, and if the vibration is transverse with charge separation the phonon is optical. In that case it is analogous in ways to the photon. There are polarons, magnons, charge density waves and so forth. The polaron is way the quantization of a lattice perturbation that renormalizes the mass of an electron and is a precursor of sort to Cooper pairs in superconductivity. In an analogous manner a graviton might be considered as the entanglement of two gauge bosons in a chargeless or "colorless" state.

  6. Dr. H, Thanks for your reference to Brilliant. It gives a more organized and in-depth way for me to absorb the meaning of many of your Blog strings than my usual necessary browse of Google. e.g., I don't remember Quantum concepts as even being part of Engineering when I got my degrees, let alone the basis of Physics.

  7. Dr. H.,
    Thanks for the link to Brilliant. Your assessment of its usefulness is spot on, for my level.

  8. Hi Sabine,
    In the comments on yr previous blog, several people remarked that for an electric charge, the equivalence principle is not valid as an accelerating charge will radiate (I think this follows from Maxwell’s laws) while a charge at rest in a gravitational field does not. Is this correct?

    1. Have you tried asking google before you expect me to spend my time on this? I am not an ask-the-expert forum.

    2. Mark Behets, here is a reference: "Falling Charges" (1964) by DeWitt and DeWitt. It is insightful, reading: "However, the equivalence principle, as dramatized by the falling elevator concept, injects an element of uncertainty and confusion into the picture. It is the purpose of this paper to remove the confusion." Also, James Anderson, 'Principles of Relativity Physics' writes: "the question, does a uniformly charged-particle radiate ? has been answered in different ways by different writers" (1967, pages 246-248). A technical, but insightful, discussion is Bryce DeWitt's Lectures on Gravitation (pages 161-172).

    3. Sorry Sabine if I’ve irritated you. Indeed you cannot be expected to answer these kind of questions, on top of the blogs and videos you produce each week for free. And Google and Gary (thanks Gary) were a great help.

    4. Gary Alan, you wrote

      >> Mark Behets, here is a reference: "Falling Charges" (1964) by DeWitt and DeWitt.

      As its title says, it is about a free falling charge. Very interesting, but this has nothing to do with the equivalence principle. Because a free falling charge is not subject to any forces. In contrast the observer in Einstein’s elevator cabin is subject to forces, either to the inertial force or to gravity.

  9. Sabine, as someone who had already subscribed to Brilliant before you mentioned it, I agree with Bert (aka KWPD) that it is a superb and worthwhile training tool.

    I was especially impressed by Brilliant’s use of drag-and-drop graphical widgets, which allow students to test their understanding of concepts in a very hands-on and instantly correcting fashion. For a student, that is a superb way to make sure you have understood a critical concept correctly. Also — and this is important — Brilliant provides coverage for areas that are not covered by the also-excellent and free (but non-interactive) Khan Academy. I have never seen anyone teach math as well as Salman Khan does, but that is also the difficulty with the Khan Academy: No one seems able to duplicate his style. In contrast, Brilliant's teaching model appears to be fully generalizable, and it also adds those marvelous interactive widgets.

  10. I saw something that showed some of the flat Earthers have graduate degrees and work as engineers. Here's a good spot to make a connection that can get overlooked. The strength of their passion for their bias is just stronger than yours (everyone). Everyone sways their beliefs and arguments towards their bias, to what extent we ignore reality when doing so it regulated by the strength of our conviction. Scientist are not immune and do it all the time too. When seeing something like this we all need to remember to constantly look inwards and police ourselves first, especially those who work in the sciences, because it so easy to fool yourself.

  11. And how long at 1 gee acceleration does "the disc" take to get to light speed?

  12. The problem with the equivalence principle is the adverb "locally" used in its definition (“Acceleration in a flat space-time is locally indistinguishable from gravity”). The adverb "locally" behaves as a wildcard. There will be always a threshold where the wildcard "locally" will prevent any theory to be falsified. In that sense, someone could also claim that the Earth is locally flat, and be right.

    1. This is just wrong. You can calculate how large the deviations are and then you know what it takes to measure them. The equivalence principle is an assumption you use to derive the theory, it is not the theory itself.

    2. If I can elaborate on Sabine's point: there is a widespread but erroneous belief that if you can prove the “principle of equivalence” to be wrong, then you have refuted General Relativity.

      In fact, the “principle of equivalence” was just a heuristic that helped Einstein guess the correct theory. Now that we have the theory, you can just ignore the “principle of equivalence” and work with the actual mathematical theory.

      If course, the “principle of equivalence” is still useful in helping students understand the theory and helping physicists think qualitatively, and the “principle of equivalence” is indeed correct if understood in the proper limiting sense.

      But, in physics, math rules. And, no, this does not mean we are “lost in math”! “Lost in math” is allowing mathematical “beauty” to trump empirical data in searching for a theory. But once you have a prospective theory, then the definitive formulation of that theory is the mathematical formulation, not some verbal statement that people can misinterpret in myriad ways.

      If there is any contradiction between GR and the “principle of equivalence,” just forget the “principle of equivalence” and go with the actual mathematical theory.

    3. Let me add a few words to what Dave said. It is correct of course that the equivalence principle was merely a way for Einstein to derive General Relativity and that today the question is whether GR is correct, not whether how Einstein came up with it is "correct". Having said that, though, a lot of tests of GR are specific tests of the equivalence principle, or at least that is what they are called, for one reason or the other. Maybe it would be better to not call them that. (There is actually some discussion in the literature as to whether it is even possible to tell apart, say, violations of the EP from violations of LI, so this is not a simple question.)

      All of this is just to say that tests of the equivalence principle do exist, so saying that one can ignore it is maybe a somewhat extreme way of phrasing the situation.

    4. PhysicistDave5:52 PM, August 04, 2020

      "But once you have a prospective theory, then the definitive formulation of that theory is the mathematical formulation, not some verbal statement that people can misinterpret in myriad ways."

      Oh, good. Then you can provide a mathematical formulation of your theory that it is impossible for the mind to be weakly emergent from a physical brain.

      Here is your theorem and proof so far:

      Dave's Theorem: The mind cannot be weakly emergent from a physical brain.

      Dave's Proof:
      Assume the mind cannot be weakly emergent from matter ----(1)

      Using (1), it follows that the mind cannot be weakly emergent from matter.


      Fascinating stuff about the EP, Dave. But everybody knows trivial stuff like that,

      and you remain a liar

      until you provide your promised "logical proof" ;)

      You don't get to tell lies and then carry on as if nothing has changed. That's not how society works.

      You are a liar, Dave.

    5. Sabine,

      I should probably have written:
      “If someone believes he has come up with a verbal or philosophical contradiction between GR and the 'principle of equivalence'...”

      If the results of an experiment convince Cliff Will (or even you or me) that the experiment is a disproof of the principle of equivalence, then GR is probably in trouble.

      But what I meant to address was the various verbal and philosophical “paradoxes,” so beloved by some commenters here, that are really just word games with no relevance to the actual physics. (Same thing holds for special relativity, as well as GR, maybe to an even greater degree.)

      By the way, some of the “paradoxes” – such as the radiating vs. non-radiating electric charge – do seem to me worth thinking about, even though they do not of course disprove GR.

      A better understanding of classical EM and of how it combines with both SR and GR seems to me a worthy enterprise, even though it will not disprove either SR or GR.

      All the best,


    6. "You don't get to tell lies and then carry on as if nothing has changed. "

      Correction - you do get to tell lies and carry on as if nothing has changed ;)

      Anyway, Dave, now that you are coming towards the end of your life, can you point me to some ground-breaking work that you've done in Physics?

      Or have you been a complete failure who is reduced to having to boast about having taken classes with Feynman 60 years ago in the comments of a blog?

    7. @Dave, @Sabine and @Steven,
      I thought I could help reduce some tension by stating: None said that GR would be disproved if an experiment appears to violate the EP. On the contrary, it will prove that GR is a subset of a wider framework.

      I predict that SR and GR are subsets of a wider framework and particularly in the case of SR I prove this mathematically (see my Profile).

      Special quasiparticles seems to be capable to reduce their effective inertia while being accelerated, something that SR cannot predict, which means SR might be a subset of a wider framework, as I present in detail along with the Lorentz transformations.

      Important Note: Einstein's SR and Lorentz original transformations remain intact (no adhoc modifications) from the beginning to end. This is something most theoretical works (not to say all) cannot do.

      It appears the wider framework to work just with quasiparticles and in case one attempts to use it for bare particles e.g. electrons, it automatically reduces to known Einstein's SR. The same is mathematically demonstrated for the Lorentz transformations wider framework.

      Besides the reduction of the effective inertia (for quasiparticles always), they are allowed to reach and even surpass the speed of light by simultaneously reducing the local speed of the propagation of the electromagnetic waves. One can use the general discovered expression (wider framework) in order to study the transition from superluminal to subluminal and vice versa or in a special case where a quasiparticle loses its properties and turns to a particle while travelling at superluminal speed.

      Furthermore, it is mathematically possible to distinguish what is violated, the constant rest inertia or the constant local propagation of the speed of light (it can be reduced down to zero but never below zero)? And as you may see certainly, the latter!

    8. Steven Evans wrote to me:
      >Anyway, Dave, now that you are coming towards the end of your life, can you point me to some ground-breaking work that you've done in Physics?

      Steve, you are getting a little bit overwrought! You're upset because I have pointed out that what you thought was a knock-down argument against religious believers does not really work.

      The odd thing is that you and I more or less agree on religious issues: I do not think God exists, I do not think that consciousness survives death, and I think that most organized religions have some serious crimes to answer for. I'm just not quite as certain as you are on some of these matters.

      To be honest, all my life I seem to have lacked the “will to believe”: when I was taught religious dogmas as a child, my instinct was to say, “Hmmm.... interesting hypothesis. Now, I wonder how we can test it to see if it is true or not?” I'm afraid that I have the same attitude towards atheist dogmas, materialist dogmas, etc. It got me in some trouble as a child, and it's making you angry now.

      Anyway, to answer your question, I have accomplished as much as most physicists and more than some: I have developed novel mathematical techniques that had significant practical applications, earned some patents, published a few papers, and so on. As I have said, I was even part of a team that won a technical Emmy from the Academy of Television Arts and Sciences in the late 1980s.

      As I think you know, by definition, very few physicists have done “ground-breaking work,” sinply because we only count a small number of achievements as “ground-breaking.” If everything were ““ground-breaking,” nothing would be ““ground-breaking.”

      I can say that nothing I have done in physics, math or engineering has turned out to be radically wrong or “not even wrong,” which is more than can be said for many physicists who are now prominent in the field.

      I have never claimed to be anything more than a simple, journeyman physicist, toiling away in the mines, hoping now and then to find a gemstone of quite modest beauty and value. That I have done, and that is all that most physicists can expect to do.

      Steve also asked:
      >Or have you been a complete failure who is reduced to having to boast about having taken classes with Feynman 60 years ago in the comments of a blog?

      When I am dealing with some crack-pot who has his own private goofy theory of QM, it is relevant that I took QM from a giant in the field. Similarly, for the fact that I took GR from Kip Thorne and QFT from Steve Weinberg.

      I suppose that you would not be so angry if you did not realize that I have indeed shown that your simplistic argument against our spiritualist friends does not work.

      There are better arguments against religion, Steve. Hume's argument against the plausibility of miracles still stands, for example.

      Anyway, like Sabine, I support freedom of expression, including your right to vent your frustration that I have shown that the mind-body problem is harder than you would like to believe.

      Significant problems usually are hard: that is part of what makes them significant.

      Thanks again for all your help in critiquing my arguments in ways that have enabled me to strengthen my arguments. J. S. Mill was right: one of the compelling reasons for freedom of expression is that correct ideas should be strengthened by serious criticism.

      All the best,


    9. John11:50 AM, August 05, 2020

      "I thought I could help reduce some tension by stating:"

      No need. What is needed is for people to withdraw dishonest claims:
      Dave Miller - claimed repeatedly to have a logical proof refuting the possibility of mind being weakly emergent from matter. No proof provided, obviously. So he's a liar.

      Phillip Helbig, Luke Barnes - claimed repeatedly to have evidence of universal fine-tuning No evidence provided, obviously. So they are liars.

      Nobel Laureate Brian Schmidt, Professor Geraint Lewis - supported Luke Barnes' lies in the comments here on Twitter (!?) and fail to deal with copious mistakes and lies in published books they have put their names to. So they are liars.

      There are liars in Physics. They should be pointed out. The above people had their "errors" pointed out to them many times and were given plentiful opportunities to withdraw them, but they continue to choose to stick by their lies.

    10. PhysicistDave7:55 PM, August 05, 2020

      Dave, you are a liar. You claim to have a "logical proof" that mind cannot be emergent from matter, but have provided no proof. Everybody can see you are a liar.

      Anyway, as you have contributed nothing to Physics of significance, why don't you tell us yet again about the classes you took with Feynman and Weinberg 60 years ago? It's truly fascinating.

      They would be really proud that their former student has become a liar.

    11. PhysicistDave7:55 PM, August 05, 2020

      "Anyway, like Sabine, I support freedom of expression,"

      I'm not sure why, but you keep mentioning Dr. H. in your replies. You're aware that she, too, knows you're a liar?

      Unless you provide a logical proof that the mind cannot be emergent from matter or withdraw your claim, you remain a liar and everyone can see it.

  13. Hi Sabine,

    flatearthers I right I think.
    They just fail to think in 4D :)


  14. Dear Mrs Hossenfelder,

    First, I read many of your publications for 'laymen' and 'laywomen', even some of your papers on the arXiv, and currently I am reading and enjoying very much Lost in Math (awesome book). Thank you very much!

    Please, I believe one should not use 'flat earthers' even as a starting point for any meaningful, science-based discussion.

    To me it is likely you will not reach those people, instead you contribute to the spreading of their nonsense, by giving credibility through referring to them.

    But maybe I am too pessimistic about this?


  15. James Hartle, a footnote, writes: "Does the equivalence principle sound mathematically imprecise to you ? It is. Principles like this (and the principle of relativity) that make statements about the laws of physics in advance of their mathematical formulation are generally so. That does not mean that they have no content."
    (2003, page 119, Gravity). Peter Bergmann presents a lucid account on the topic in chapter ten of his Introduction to the Theory of Relativity (1942, an oldie, but a goodie). Clifford Will writes: "The Einstein equivalence principle is the foundation of all curved spacetime or 'metric' theories of gravity, including general relativity." (1981 first, page 22, Theory and Experiment in Gravitational Physics).



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