Superluminal Travel from Quantised Inertia

[Mark7777777]

A new article has been posted in the Journal of Space Exploration regarding a Quantised Inertia FTL travel theory.

Author:
Michael Edward McCulloch
University of Plymouth, Plymouth, PL4 8AA, UK

https://www.tsijournals.com/articles/superluminal-travel-from-quantised-inertia.pdf


Abstract

Special relativity predicts that the inertial mass of an object is infinite at the speed of light (c) causing zero acceleration and producing a cosmic speed limit. Here, a new model for inertia is presented that challenges this. The model (quantised inertia) assumes that inertia is caused by Unruh radiation made inhomogeneous in space by relativistic horizons. Quantised inertia is consistent with standard physics at normal accelerations, but predicts a new loss of inertia at very low accelerations, predicting galaxy rotation without dark matter and a minimum acceleration of 2c2/Θ ~ 2 × 10-10 m/s (where Θ is the co-moving Hubble diameter) which is equal to the cosmic acceleration and that persists even at the speed of light. This implies that the speed of light limit can be broken, albeit with this tiny acceleration and that this relativity - proof acceleration could be boosted by setting up a causal horizon around the ship.
Keywords: Unruh radiation; Quantised inertia; Faster than light travel

[speedevil]

acceleration of 2c2/Θ ~ 2 × 10-10 m/s (where Θ is the co-moving Hubble diameter) which is equal to the cosmic acceleration and that persists even at the speed of light. This implies that the speed of light limit can be broken, albeit with this tiny acceleration and that this relativity - proof acceleration could be boosted by setting up a causal horizon around the ship.

Units matter.
That is three hundred years to accelerate 1m/s.
To change speed by 1% of c would take a billion years.

[meberbs]

Now that there is a separate thread on this, I will list some of the many problems with McCulloch's theory (only some, because there are a ton)

-The basic inertial mass equation in his theory divides by acceleration, which has obvious divide by 0 problems. Actually, for any acceleration less than 2*10^-10 m/s², it implies negative inertial mass.
-Setting force to 0 in his equation 11 also brings up problems with this, causing the acceleration to be equal to a fixed 2*10^-10 m/s². This makes the inertial mass in his theory 0, which by special relativity, means the particle must be moving at the speed of light.
-I have not seen anything where he reconciles basic conservation laws with his claims, considering that he claims to explain propellantless thrusters which break conservation of energy and momentum, the answer seems to be it doesn't.
-On a similar note, general relativity is based on the principle that inertial and gravitational mass are the same. I have not seen any explanation of how to handle GR effects under McCulloch's theory, nor any demonstration that McCulloch's theory can replicate the standard tests of GR.
-He says "The  consequences of the FTL discussed here for causality are complex, and have not yet been considered." The consequences are actually quite simple, he does not modify the time dilation parts of special relativity, so this would simply break causality. Another thread on here has gone into the FTL causality problem in detail, and it basically boils down to you need to define a universal reference frame that FTL is restricted to be relative to. McCulloch's theory does not appear to contain any such thing.
-McCulloch's theory has essentially already been falsified due to his many claims of things it is supposed to explain. Notably, this includes the Pioneer anomaly. He has an old blog post where he complains about the resolution of the pioneer anomaly, but all he does in it is demonstrate his ignorance of thermal modelling.
-Other predictions include the emDrive and Mach effect, which aren't looking so good (see relevant threads to discuss each of those.)
-In general, McCulloch fails to provide numerical predictions to accompany his claims, which in itself is a red flag, one reason he doesn't provide numbers may be provided by the next bullet.
-McCulloch likes to claim his theory doesn't have adjustable parameters, but it contains one number which is not a fundamental constant, the cosmic diameter (why not radius?) many of his claims are based on the undefined nature of how to calculate that parameter, and it seems he basically handwaves changes to it any time he needs a different result.
-Also as initially pointed out by others in the emDrive thread before this topic was split off, McCulloch's paper only addresses circular accelerators, not linear ones, and he has provided no numbers to support his claim on Twitter that the acceleration profile in linear accelerators is such that the effects of his theory would not be seen. Ina linear accelerator, the acceleration is only in the direction of motion, so his previous calculations apply, which say that the acceleration would not stop, and the speed of light would be exceeded. Even in the example in the paper, he does not do the math completely, since the LHC beams are around 0.99999999 c (~3 m/s short of c) so the amount of relativistic mass increase is huge, and even a small proportional decrease in mass could be significant. Also, he comes to his conclusions based on a Taylor series that is not a good approximation for near c. I have attached a plot from wolfram alpha showing the curved blue dotted line diverges significantly from the correct expression as v/c-> 1. https://www.wolframalpha.com/input/?i=sqrt(1-x%5E2)+taylor+x%3D0
-Also, as an example of how McCulloch changes constant in his theory in an arbitrary way, for something like the emDrive, and his proposals to improve the FTL drive, shielding magically makes the divide by the size of the universe scale factor change to something helpful. He does not apply this same reasoning to particle accelerators, which are sealed metal vacuum tubes, because then it would be clear how wrong his theory is.

In summary: McCulloch's theory is completely inconsistent, and seems to me to be beyond hope of rescue.

Edit: typos, and fixed the link

[MikeMcCulloch]

Reply to meberbs' crit. Note that these are brief replies (all I can give at the moment):
- The negative inertial mass would never be reached because as the QI-predicted inertia approaches zero the acceleration increases again. The result is an acceleration that asymptotes to 2x10^-10 m/s^2.
- Setting F=0 in equation 11 predicts the minimum acceleration of 2c^2/Theta which is the main prediction of QI. It is due to the attraction of the cosmic horizon, is fueled by information (see below) and is supported empirically by the supernovae data (Perlmutter and Riess, 1999). It is the value of the observed cosmic acceleration.
- QI does not conserve mass-energy, but it does conserve mass-energy-information. In QI information can be converted to mass-energy and vice versa. This is directly related to Landauer's principle which has been verified.
- I am not so worried about agreement with GR because it has been falsified. Ie: it has never predicted a single galactic rotation correctly. I am working on a paper using Qi to predict the bending of star light round the sun.
- As I said, I have not considered causality yet. QI does not depend on reference frames because it uses accelerations. These are independent of ref frame.
- The Pioneer anomaly has not been falsified. The modelling of known anomalies with a complex model is a disease of modern physics. Dark matter is the same.
- 'Fails to provide numerical predictions'. Are you joking? I always make numerical predictions.
- The cosmic horizon is not an adjustable parameter. Sure it has an allowed range, but that is small and known.
- In QI it does not matter whether the acceleration is linear or circular. I performed the calculation for circular accelerators, but linear ones still accelerate at a huge rate so the effect of Qi will be tiny.
- The Unruh waves for particles in accelerator tubes will not interact with the tubes in the same way as for the emdrive, because in the emdrive the microwaves are finely tuned so that the Unruh waves are exactly the right size to resonate in the cavity.
- In summary. QI is not complete and I am not claiming for sure that every anomaly I have looked at is valid, but QI predicts the more conclusive ones, eg galaxy rotation, in a simpler, more elegant manner than any other theory.

[meberbs]

- The negative inertial mass would never be reached because as the QI-predicted inertia approaches zero the acceleration increases again. The result is an acceleration that asymptotes to 2x10^-10 m/s^2.

I don't think you meant to type that the acceleration "increases again", the asymptotic comment is the correct description of taking the limit of equation 11 as force approaches 0.

- Setting F=0 in equation 11 predicts the minimum acceleration of 2c^2/Theta which is the main prediction of QI. It is due to the attraction of the cosmic horizon, is fueled by information (see below) and is supported empirically by the supernovae data (Perlmutter and Riess, 1999). It is the value of the observed cosmic acceleration.

You are missing the point, acceleration in what direction? If there is a force, the acceleration is in the direction of the force if there is none, then there is no definition in your theory for the direction of acceleration. The accelerating expansion of the universe is an entirely different type of phenomenon than the local acceleration of a given mass that the equation you used describes.

- QI does not conserve mass-energy, but it does conserve mass-energy-information. In QI information can be converted to mass-energy and vice versa. This is directly related to Landauer's principle which has been verified.

If that is the case, please provide a rigorous explanation of how that works (It seems to me this would not work for various reasons, but rather than speculating I should see what the details are of your explanation, in case you did find some way that I can't think of.) this only covers energy conservation, which is tied to time symmetry in Noether's theorem, you also need something to cover momentum conservation, which your theory also clearly violates.

- I am not so worried about agreement with GR because it has been falsified. Ie: it has never predicted a single galactic rotation correctly. I am working on a paper using Qi to predict the bending of star light round the sun.

GR has not been falsified, your assertions that is has are part of what quickly loses you credibility when you talk to other scientists. GR predicts galactic rotation curves just fine under lambda-CDM, which is a model that has been tested including things such as the evolution of the universe over time to form galaxies as we currently observe them. Also, before you mention it, wide binaries have previously been discussed on this site. A recent paper shows that the data is actually consistent with GR, the pattern in the data is related to projection effects.

Anyway, as I said, you confirm here that you have not actually compared to your theory with any of the standard tests of GR yet. The various claims you make promoting your theory make it sound like it has wider applicability than GR, but in actuality, you have not shown it matches with any of the experimental tests of GR. I (and probably most other people with a relevant background) find this strange, because if someone comes up with a new theory of gravity, the very first question is whether it can predict the results of the various experiments confirming general relativity. Since your theory fundamentally contradicts the most fundamental assumption in GR, this is even more important because it is difficult to see how such a radically different theory can replicate all of the successes of GR.

- As I said, I have not considered causality yet. QI does not depend on reference frames because it uses accelerations. These are independent of ref frame.

Your statement about being independent of reference frame is the basis of why I said it is simple: Your theory breaks causality.
Your claim of frame independence actually brings up one of the issues I didn't address before:
acceleration on its own is not a relativistic invariant, you need to consider the four acceleration, which you do not address in your paper.

- The Pioneer anomaly has not been falsified. The modelling of known anomalies with a complex model is a disease of modern physics. Dark matter is the same.

The pioneer anomaly is not resolved with complex physics, but simple physics which has been known and tested for a long time: the momentum carried by electromagnetic waves, and the power  proportional to T^4 of black body radiation.

I previously read a blog post from you on the Pioneer anomaly and you basically had 2 points:
-The thermal model had a couple adjustable parameters correlated to the spacecraft data
This is standard practice in thermal modelling of spacecraft, some details of reality are not going to be accurately predicted by the model, so you adjust these to match with the as measured temperatures. Since these are correlated with temperature, not with the thrust, this in no way invalidates their predictions. It actually supports the validity.
-You complain about there being "thousands" of finite elements which only shows that you don't understand the basics of this well used and effective modelling technique.

- 'Fails to provide numerical predictions'. Are you joking? I always make numerical predictions.

You mean like the predictions you have provided for the upcoming tests of your theory?
https://twitter.com/memcculloch/status/1127923530799222785
Actually I couldn't find those predictions, and your tweet is backwards anyway. If you make a prediction for both unless both produce thrust consistent with your predictions, your theory is wrong. Claiming you are validated if either produce any thrust is a form a cherry picking.

Let's look at a previous list of "predictions" you made:
http://physicsfromtheedge.blogspot.com/2016/04/predictions-of-mihsc.html
1, 4, 5, 6, 7, 11, 12, 15, 16 don't have numbers. That is more than half. You can argue that there is reasons for some of them, but even predictions like numbers 2 and 3 have an acceleration in them, but are actually incredibly generic, and describe a qualitative effect with no real world examples provided.

- The cosmic horizon is not an adjustable parameter. Sure it has an allowed range, but that is small and known.

You hypothesize changes to it all the time when you want a different result. When you compare the size of the observable universe and the speed of light, it is not surprising when you end up with a number related to the rate of expansion of the universe. Please point to a rigorous derivation of why the size of the universe is the relevant number, you ignored the question in my post on why it is diameter rather than radius.

- In QI it does not matter whether the acceleration is linear or circular. I performed the calculation for circular accelerators, but linear ones still accelerate at a huge rate so the effect of Qi will be tiny.

Again, you provide no numbers to support your claim even after being directly prompted for them. Towards the end of the accelerator, the inertial mass would increase reducing the acceleration.

- The Unruh waves for particles in accelerator tubes will not interact with the tubes in the same way as for the emdrive, because in the emdrive the microwaves are finely tuned so that the Unruh waves are exactly the right size to resonate in the cavity.

Take a look at bullet point number 11 from your post I linked to. You specifically claimed the waves in an accelerator would be shortened, which would increase the effect of your theory. Again, you are just picking and choosing assumptions to fit whatever suits you at the moment.

- In summary. QI is not complete and I am not claiming for sure that every anomaly I have looked at is valid, but QI predicts the more conclusive ones, eg galaxy rotation, in a simpler, more elegant manner than any other theory.

No physics theory is complete, we do not have a theory of everything. However you claim to be replacing GR, and have yet to successfully replicate a single one of its predictions. Your theory currently does not appear to even be fully rigorous or consistent, so calling it "simpler" is misleading. Not everything in the universe is simple, and insisting on a simple explanation of inherently complicated things just means being wrong. There is nothing elegant about breaking causality, which is what FTL means, unless a universal reference frame is defined.

Also I am cautious about bringing this up, since I don't want you take take this as an invitation to talk about some of the things you say on social media, which are counterproductive to having a reasoned conversation. I did some basic research on the journal you published papers in. A known problem with modern scientific publishing is that there are a large number of predatory journals out there that take advantage of the pressure for academics to publish and charge high fees for publication, often not performing proper peer review even if they claim to. Someone went to the trouble to compile a list and it was no surprise to find the one you are using is one of them: https://scholarlyoa.com/publishers/

As I pointed out (but you failed to address) You have a major mathematical error in your paper where you apply a low velocity Taylor series approximation of relativity to extremely high velocities where the series is not close to converging for the terms you used. Anyone with a mathematical background should be able to notice this error, and the approximation is so common in relativity, any competent reviewer with an appropriate background would immediately notice that error. This indicates that the journal you are using at best only pretends to do peer review. I recommend doing some research and finding an actually respected journal to get published in if you care to be taken seriously. (Due to that error alone your paper as currently written could make a good test for the peer review quality of relevant journals.)

[Cryogenic]

I'm not a physicist, so here's my (limited) understanding of this:

You are missing the point, acceleration in what direction? If there is a force, the acceleration is in the direction of the force if there is none, then there is no definition in your theory for the direction of acceleration. The accelerating expansion of the universe is an entirely different type of phenomenon than the local acceleration of a given mass that the equation you used describes.

From my understanding, The acceleration is in the direction o movement. And that direction could be any referential frame you are using, like a gravitational orbit. If theoretically there would be no frame of reference then the direction of acceleration would be Random, like a quantum fluctuation. (This is my understanding at least)

If that is the case, please provide a rigorous explanation of how that works (It seems to me this would not work for various reasons, but rather than speculating I should see what the details are of your explanation, in case you did find some way that I can't think of.) this only covers energy conservation, which is tied to time symmetry in Noether's theorem, you also need something to cover momentum conservation, which your theory also clearly violates.

QI redefines momentum as Unruh radiation pressure of Rindler horizon. So of the universe expands the radiation pressure decreases, momentum also decreases. QI ties momentum to Rindler Horison and universe scale. When universe size approaches zero, momentum approaches infinity, and when the distance between any particles in the universe approaches infinity momentum approaches zero. Please correct me if I'm wrong.

GR has not been falsified, your assertions that is has are part of what quickly loses you credibility when you talk to other scientists. GR predicts galactic rotation curves just fine under lambda-CDM, which is a model that has been tested including things such as the evolution of the universe over time to form galaxies as we currently observe them. Also, before you mention it, wide binaries have previously been discussed on this site. A recent paper shows that the data is actually consistent with GR, the pattern in the data is related to projection effects.

GR was never proven at the galactic scale. GR is still an unproven theory at the galactic scale. (If it's proven why do scientists spend billions on Dark Matter searches? To prove what?)

Anyway, as I said, you confirm here that you have not actually compared to your theory with any of the standard tests of GR yet. The various claims you make promoting your theory make it sound like it has wider applicability than GR, but in actuality, you have not shown it matches with any of the experimental tests of GR. I (and probably most other people with a relevant background) find this strange, because if someone comes up with a new theory of gravity, the very first question is whether it can predict the results of the various experiments confirming general relativity. Since your theory fundamentally contradicts the most fundamental assumption in GR, this is even more important because it is difficult to see how such a radically different theory can replicate all of the successes of GR.

As MikeMcCulloch has put it. The challenge of #QI to GR is not at high accelerations, but at extremely low accelerations where GR has failed to predict Galaxy rotations without arbitrary additions of Darm Matter. This Dark Matter is a purelly hypothetical substance with no predictable properties. Does not fit the standard model, does not interact with anything (and I don't mean only light, anything, any matter. DM detector experiments were all failures), it's at this point a figment of imagination at best (that is if you're a normal human, not a scientist, and use basic logic here)

Your statement about being independent of reference frame is the basis of why I said it is simple: Your theory breaks causality.
Your claim of frame independence actually brings up one of the issues I didn't address before:
acceleration on its own is not a relativistic invariant, you need to consider the four acceleration, which you do not address in your paper.

Would you provide some arguments to these claims? I'm not a scientist so I would appreciate if you'd detail more what exactly are you referring to here.

[MikeMcCulloch]

meberbs. I have replied to a few of your comments, but as you will see, I stopped when I noticed that your comments were straying towards attacking my motivation & the state of modern journals. If you can't attack QI itself with solid physical evidence and you have to start digging around for other ways to undermine it, then I've learned from many long and painful experiences that the debate quickly deteriorates.

1. The direction of the extra QI acceleration is in the direction of acceleration.
2. The conservation of mass-energy-information is explained in this paper by myself and J. Gine: https://www.worldscientific.com/doi/abs/10.1142/S0217732317501486
3. GR has been falsified. We have to call a spade a spade, and GR has never, ever predicted a galaxy rotation correctly without 'tuning' of the data after the fact (ie dark matter). GR is wrong. It is as simple as that. I've published three papers on galaxy rotation now, and I'll be publishing another paper soon on wide binaries that confirms that.
4. The Pioneer anomaly has been modelled with a complex thermal model with over 2000 finite elements and two adjustable parameters. That's complex in my book.
5. Yes, I have made predictions, but you have to read my papers to see most of them.
6. The 8.8x10^26 m diameter of the cosmos is the currently accepted value for its size, given the need to also include inflation to explain the flatness problem. It is widely accepted, see eg Bars and Terning, 2009. extra Dimensions of Space and Time, Springer.

[meberbs]

From my understanding, The acceleration is in the direction o movement. And that direction could be any referential frame you are using, like a gravitational orbit. If theoretically there would be no frame of reference then the direction of acceleration would be Random, like a quantum fluctuation. (This is my understanding at least)

This would contradict McCulloch's statement further down that his theory is reference frame independent. Predicting different acceleration direction depending on what frame you are looking from means your theory is simply inconsistent.

QI redefines momentum as Unruh radiation pressure of Rindler horizon. So of the universe expands the radiation pressure decreases, momentum also decreases. QI ties momentum to Rindler Horison and universe scale. When universe size approaches zero, momentum approaches infinity, and when the distance between any particles in the universe approaches infinity momentum approaches zero. Please correct me if I'm wrong.

This does nothing to address my question, and if accurate demonstrates the lack of conservation of momentum.

GR was never proven at the galactic scale. GR is still an unproven theory at the galactic scale. (If it's proven why do scientists spend billions on Dark Matter searches? To prove what?)

Falsified means proven to be wrong. "Not proven" does not equal "falsified." GR with dark matter successfully explains galactic scale gravity. The properties of dark matter are such that we are certain that it is difficult to detect. It possibly only interacts via gravity, in which case it will never be detected through its gravitational influence. We don't know know if this is the case or not, so scientists look for it (Also, I haven't heard of any dark matter searches costing billions, there are few science projects that get that level of funding, like the LHC or NASA's great observatories, and those generally have other purposes. Sure physicists hope that they might get lucky and find a candidate dark matter particle at the LHC, but it is primarily designed around resolving questions about the standard model of particle physics, which scientists are quite sure is at best incomplete, but experiments keep stubbornly agreeing with it, because so far none have found the scale where it breaks down.)

As MikeMcCulloch has put it. The challenge of #QI to GR is not at high accelerations, but at extremely low accelerations where GR has failed to predict Galaxy rotations without arbitrary additions of Darm Matter.

If that is the goal, then McCulloch's theory amounts to nothing other than an empirical model. The actual useful goal is a theory that has a larger region of applicability than existing theories.

This Dark Matter is a purelly hypothetical substance with no predictable properties. Does not fit the standard model, does not interact with anything (and I don't mean only light, anything, any matter. DM detector experiments were all failures), it's at this point a figment of imagination at best

All wrong, Lambda-CDM has specific properties of dark matter specified that predict not just galactic rotation, but also the evolution of the universe and the formation of galaxies. There is also evidence that not all galaxies have the same amount of dark matter in them, though most are very similar as would be expected. As explained above, there are reasons for scientists to believe the standard model is incomplete from within the standard model, not because of dark matter. Also as explained above, dark matter interact with all matter through gravity, but there is no reason to believe that it interacts through any other force (and inherent reasons that it definitely does not interact through electrodynamics, so it is not surprising that it has not been detected directly.)

(that is if you're a normal human, not a scientist, and use basic logic here)

Science is based on basic logic. What you are doing here is effectively claiming that every scientist on the planet is an idiot (at best) One warning:conspiracy theories and insults are not accetable forms of conversation on this site.

Your statement about being independent of reference frame is the basis of why I said it is simple: Your theory breaks causality.
Your claim of frame independence actually brings up one of the issues I didn't address before:
acceleration on its own is not a relativistic invariant, you need to consider the four acceleration, which you do not address in your paper.

Would you provide some arguments to these claims? I'm not a scientist so I would appreciate if you'd detail more what exactly are you referring to here.

The fact that FTL breaks causality is a topic covered in any introductory class on special relativity. Details have been discussed in a separate thread on this site:
https://forum.nasaspaceflight.com/index.php?topic=43385.0

[meberbs]

meberbs. I have replied to a few of your comments, but as you will see, I stopped when I noticed that your comments were straying towards attacking my motivation & the state of modern journals.

I did not attack your motivation, period. Anywhere you think I did so, you misread the intent of what I wrote. I would appreciate if you could let me know specifically where this happened, preferably via PM to keep the thread on topic, and I can work to make sure such confusion does not happen again, and modify the original statement if appropriate.

The comment about journals is to inform you of some information that would help you, (among other ways by not sending money to probable scammers.) The existence of predatory journals is a well known fact. Here is the most recent example I have seen. (warning: contains repeated profanity)

If you can't attack QI itself with solid physical evidence and you have to start digging around for other ways to undermine it, then I've learned from many long and painful experiences that the debate quickly deteriorates.

I gave direct criticisms of your theory. A few points I made also include suggestions on what you can do to improve the credibility of your theory. As far as the conversation deteriorating when you go to non-technical attacks, I suggest you review some of what you have posted on social media in light of that. Those specific comments are not appropriate for discussion here. (PM me if you can't figure out what I am talking about.)

1. The direction of the extra QI acceleration is in the direction of acceleration.

When there is no force, this is a tautology and undefined.

2. The conservation of mass-energy-information is explained in this paper by myself and J. Gine: https://www.worldscientific.com/doi/abs/10.1142/S0217732317501486

Thank you, I will review when I have time.

3. GR has been falsified. We have to call a spade a spade, and GR has never, ever predicted a galaxy rotation correctly without 'tuning' of the data after the fact (ie dark matter). GR is wrong. It is as simple as that. I've published three papers on galaxy rotation now, and I'll be publishing another paper soon on wide binaries that confirms that.

You can publish infinite papers on galaxy rotation, but unless you show that galaxy rotation cannot be explained by the existance of matter with a specific set of properties (which includes not interacting electrodynamically), then your statements about falsifying GR are just wrong. As I state in my previous post, there are other reasons the standard model is believed to be incomplete, so not being in the standard model doesn't matter.

Also, before publishing any papers on wide binaries, you should read this paper:
https://arxiv.org/abs/1810.13397
It shows quite clearly that the available data is consistent with GR. The approximation of the relationship between azimuthal velocity and separation as seen from Earth breaks down due to projection effects. The available data is consistent with GR. Not all pairs available have the radial data needed to correct for the projection effects, and given that the result of the shape of the corrected prediction graph depends on the uncertainty in the radial data (which is variable), it seems unlikely that further meaningful tests of whether the data is consistent with GR can be done anytime soon. (Though maybe someone can come up with a clever statistical method to show something.

4. The Pioneer anomaly has been modelled with a complex thermal model with over 2000 finite elements and two adjustable parameters. That's complex in my book.

There is no indication that this model is any more complex than the physical geometry and thermal properties of the spacecraft itself, as I said above, the adjustable parameters exist to allow better modelling for when the complexity of the real spacecraft exceeds the model's capability to reliably predict. No matter how many times you ask for it, modelling the spacecraft as a spherical cow will not give you meaningful results.

5. Yes, I have made predictions, but you have to read my papers to see most of them.

Can you share some? A particularly relevant one I am pretty sure isn't in any paper yet published is the ones for the tweet I linked to. It would be good to see your predictions before any experiment is run.

6. The 8.8x10^26 m diameter of the cosmos is the currently accepted value for its size, given the need to also include inflation to explain the flatness problem. It is widely accepted, see eg Bars and Terning, 2009. extra Dimensions of Space and Time, Springer.

I am not asking about the experimentally measured value of the parameter. I am asking for the derivation of why it shows up in your theory in the form that it does.

[JohnFornaro]

You can publish infinite papers on galaxy rotation...

For all of you galaxy rotaters out there:

http://www.illustris-project.org/media/

[MikeMcCulloch]

meberbs. To take your points backwards, because why not:
6. The cosmic size shows up as a diameter in the derivations, but it does not matter. All I'm saying is that the longest allowed Unruh wave must be twice the cosmic diameter, or 4 times the radius. This is basic cavity physics.
5. For the Madrid experiment the prediction is ~1microN. The Dresden experiment has not yet been built. We expect more like a mN but it will depend on the exact configuration.
4. It is, shall we say, not ideal, to use complex computer models to fit known results. Also, a Pioneer anomaly of the same size was also seen in the Ulysses spacecraft which had a different shape.
3. Wide binary stars simply cannot be modelled with GR, dark matter or MoND. So these hypotheses have been falsified. Also, the galactic problems all start at the exact galactic radius where Unruh waves reach the cosmic scale. That is clear evidence for QI.
2. Do read the paper.
1. When there is no force then I would expect the anomalous acceleration to be towards the cosmic edge.

[meberbs]

meberbs. To take your points backwards, because why not:
6. The cosmic size shows up as a diameter in the derivations, but it does not matter. All I'm saying is that the longest allowed Unruh wave must be twice the cosmic diameter, or 4 times the radius. This is basic cavity physics.

Can you point me to a paper where you do this derivation or not?

5. For the Madrid experiment the prediction is ~1microN. The Dresden experiment has not yet been built. We expect more like a mN but it will depend on the exact configuration.

Thank you

4. It is, shall we say, not ideal, to use complex computer models to fit known results. Also, a Pioneer anomaly of the same size was also seen in the Ulysses spacecraft which had a different shape.

You still don't seem to understand, the only fitting done was to known spacecraft temperatures. Besides which, using a model comparably complex to the spacecraft itself is the only way to get real answers. Models like these are used for the design of all spacecraft, they work.

As for the Ulysses spacecraft, using numbers quoted from your blog:
Uluyses:12+/-3x10^-10 m/s^2 towards the Sun
Pioneer anomaly of 8.74+/-1.33x10^-10 m/s^2
12 is 25% larger than 9. That is a reasonable difference for different spacecraft with different shapes, masses, and temperature distributions. Meanwhile, do you have calculations showing what you predict for these anomalies?

3. Wide binary stars simply cannot be modelled with GR, dark matter or MoND. So these hypotheses have been falsified. Also, the galactic problems all start at the exact galactic radius where Unruh waves reach the cosmic scale. That is clear evidence for QI.

So I take it you did not read the paper I linked. Wide binary stars were modeled in GR with no issues. Your statements here are wrong. You don't even acknowledge what I wrote, and just repeat your incorrect claims as if it will become true if you say it often enough.

2. Do read the paper.

I will, though so far you aren't showing equivalent consideration on your end. Go read the paper I linked, before you dig yourself into a deeper whole with your false assertions.

1. When there is no force then I would expect the anomalous acceleration to be towards the cosmic edge.

That is a non-statement, the "cosmic edge" is in all directions.

Meanwhile, I have now mentioned twice about a simple, straightforward mathematical error in your paper (The part about Taylor series). I have not considered the consequences of doing the math correctly, since that is your job, it might even support your point, but you have completely ignored 2 mentions of it. Between this and you ignoring the paper I linked to, you aren't showing much interest in having a conversation or considering that you might actually be wrong.

[JohnFornaro]

A deeper whole...

We all do get to tease you from time to time.

[MikeMcCulloch]

meberbs. There's nothing wrong with my binomial approximation. For v=0.9c the error is about 30%, but that is compared with a predicted difference of 22 orders of magnitude or 1000,000,000,000,000,000,000,000% !!!

[meberbs]

meberbs. There's nothing wrong with my binomial approximation. For v=0.9c the error is about 30%, but that is compared with a predicted difference of 22 orders of magnitude or 1000,000,000,000,000,000,000,000% !!!

30% is well outside the range where a Taylor series is considered a useful approximation.

You state in your paper "when v is higher still, the effect of QI decreases even further." Here you are taking the limit as the error in the approximation you are using is approaching either 100% or infinity % depending on which way you define your error. As I pointed out, the relevant velocity in the LHC should be somewhere around 0.99999999 c. At that point the Taylor series is off by orders of magnitude.

There doesn't seem to be any actual point to your taking of a Taylor series, since sqrt(1-x^2) is not a difficult formula to calculate. I have no clue why you seem so resistant to fixing this simple mistake. Also, it seems strange that you would take the ratio of the relativistic contribution and your contribution to determine detectability. The only thing that should matter is the magnitude of the your effect. Your modification is multiplied by the total relativistic mass, which directly changes the energy and momentum, and that would potentially be detectable when they do the careful energy and momentum balances of the results of particle collisions, or possibly through issues with the beam timing. I don't know if it would be detectable or not since you don't actually consider the sensitivity of possible detection mechanisms relative to the magnitude of your effect.

[meberbs]

I have now gone through the paper on quantized inertia and conservation of energy:

I find issues with the justification section for the new form of the energy balance, but I won't address those directly since a better justification can be written if it turns out the proposed new conservation law works as advertised.

The proposal is in equation 2:
m₁c² + kTN₁ ln 2 = m₂c² + kTN₂ ln 2

I assume that the m₁ and m₂ terms are relativistic mass rather than rest mass, to be a full account of mass-energy, including kinetic energy.

An interesting thing to note about the above equation is the k*N*ln(2) potion of the energy released into entropy terms. this can be rearranged to say k*ln(2^N) = k*ln(Ω ) = S. In this equation Ω is simply the number of available microscopic states, and S is simply the total entropy of the system. The first step is clearly the origin of Landauer's principle, as all it does is convert the number of states into units of bits. The resulting equation is literally the definition of entropy. This is where it begins to look like there may be a major problem, since entropy can never decrease, mass-energy must continuously be decreasing in the universe. This is disturbing, but lets work an example to see how this works out and see if it can make sense.

First I will rewrite the above equation based on the definition of entropy. This simplifies things, so I can just reference standard delta-entropy calculations and avoid the cosmological horizon method of calculating entropy used in the paper (which I have doubts about but again will skip over since it does not affect what I am doing.)

m₁c²+ S₁T = m₂c²+ S₂T

As in McCulloch's equivalent of this equation I simply will assume that temperature is a constant everywhere for the purposes of this example.

Now to setup the system:
Lets stake a simple "rocket" that is 2 masses, a large mass M₁ and a much smaller mass M₂, separated by a (nearly massless) spring, which for good measure we attach to the large mass. When a latch is released, they push away from each other with a constant force F for a distance d, (the spring has a very special design so that I don't have to deal with variable acceleration.)

The energy stored in the compressed spring, F*d is added to the rest mass of the large mass (M₁+F*d)*c²

Using standard physics, the result is as follows: (skip ahead for the version using McCulloch's theory)
initial energy:
(M₁+F*d/c^2)*c² + M₂*c²

The equation of motion using special relativity is given here I could skip this, since to make McCulloch's effect significant a low acceleration and low velocity limit is appropriate. Additionally, the m₀ in the linked equations for the large mass actually should account for the decreasing rest mass due to the release of the potential energy in the spring. This I will neglect, for similar reasons to the spring itself originally being essentially massless (don't want to have to account for the different parts of the spring having different velocities)

defining A = M₁*c / F, and B = M₁*c / F
You can solve for t
d = (c/A)*(sqrt(1+A^2 t^2)-1)+(c/B)*(sqrt(1+B^2 t^2)-1)
The result is a bit messy in the full relativistic form, but it is what it is. At this point, it is a it easier to treat t as the input value, with d being calculated from t as above.

The momentum of each mass after a time t is simply p=F*t, both masses have equal and opposite momentum as expected due to momentum conservation.

The total energy of the system after acceleration is:
sqrt(p²c²+M₁² c⁴)+sqrt(p²c²+M₂² c⁴)

This looks fairly different from the original expression for the energy, but lets plug in the expression for d in terms of t into the original expression, multiplying through the F/c^2, this causes terms qual to -M₁ c² and -M₂ c² to nicely cancel things out
M₁ c²sqrt(1+(F t/(M₁ c))²) + M₂ c²sqrt(1+(F t/(M₂ c))²)

Pulling the m c² into the sqrts, and you can see you get the same energy as the final result.

Now lets try that again using McCulloch's theory
First problem: what is the starting energy?
This is basically a great big divide by zero error. McCulloch gets around this by deciding that there is a minimum acceleration, in some direction he has yet to define. At this minimum acceleration value, the (1-2c²/(aΘ)) is equal to 0. McCulloch multiplies this by relativistic mass in his recent paper, so it is quite clear that this multiplies the portion of the rest mass of the large mass that is due to the potential energy of the spring. That makes the initial energy very easy to calculate:
T*S₁
With no rest mass, there is no kinetic energy, and there is no potential energy either when dealing with relativity since then you would have rest mass.

Since in this state there is an acceleration happening in an unknown direction, lets move on to the instant after the latches are released, before the systems starts accumulating any significant velocity:
Now the energy in the system is:
(1-2c²/(a₁Θ))*(M₁+F*d/c^2)*c² + (1-2c²/(a₂Θ))*M₂*c² + T*S₁

We can assume the latches are small and reversible, so entropy hasn't changed yet, though the spring is about to start doing finite work in finite time, which will increase entropy. Already this proposal for a conservation law fails, it just proved to describe a non-conserved quantity.

[I will come back later to address the state of the system during the last instant of acceleration, for now note that the extra factor applied to the potential energy of the spring will prevent the cancellation that made the case come out nicely in standard physics. Also, note that in now matters significantly which mass the nearly massless spring is glued to, because it has a different acceleration environment in each case]

Moving on to just after the last instant of acceleration, again rest masses drop back to 0, however the total mass-energy information is now:
T*S₂

This is increased from the original state, again demonstrating that Equation 2 of the paper is wrong and does not describe a conservation law.

[MikeMcCulloch]

To quote meberbs: "This is where it begins to look like there may be a major problem, since entropy can never decrease, mass-energy must continuously be decreasing in the universe".

I appreciate the thought that went into the derivation, but it is wrong from the beginning because you assumed  that entropy is solely related to the arrangement of bits on the horizon (the kTNln2 term). This is wrong, because the entropy that has been proven to increase is the entropy of the mass-energy part that we can see/detect (the other term), and your derivation ignores its contribution to entropy completely. The derivation is otherwise interesting, but needs rehashing.

[meberbs]

To quote meberbs: "This is where it begins to look like there may be a major problem, since entropy can never decrease, mass-energy must continuously be decreasing in the universe".

I appreciate the thought that went into the derivation, but it is wrong from the beginning because you assumed  that entropy is solely related to the arrangement of bits on the horizon (the kTNln2 term). This is wrong, because the entropy that has been proven to increase is the entropy of the mass-energy part that we can see/detect (the other term), and your derivation ignores its contribution to entropy completely. The derivation is otherwise interesting, but needs rehashing.

What you just stated is inconsistent with the definition of N in your paper. you defined it as:"for a system that changes its information content from N₁ to N₂" The information content of the system is related to its actual physical entropy, and it is not related to the number of Planck areas on the cosmological horizon. This is obvious because a system of 2 atoms will generally have much lower information content than a system of 1000 or 6.022*10^23 atoms. Te information content actually within the system at least is a reasonable definition fo something to try to fit into a conservation law, the new definition you just proposed couldn't even be applied to the situation I just described because different accelerations are present within the system, so there is no single way to do an equivalent of what you do in the paper and apply it to the system.

I still intend to show the step I skipped over, since I believe that will be interesting, but it seems clear at this point that you don't actually have a solution to conservation laws (energy or momentum) within your theory. Your paper essentially seems to attempt to re-derive your theory using a different method, and even then , you only get something similar, not the same. What you actually need to do is a calculation like the ones I did to show that you have working conservation laws. (Actually a general proof would be preferred, but a good example is a good place to start.) Ultimately this is your responsibility to show, as it is your theory. I see no reasonable way to fix your theory, so I can't help with that.

There is a simple prerequisite in science for new theories: they have to be consistent with what we already know. That means for a theory like yours, it has to match conservation laws, and it has to be able to replicate the standard tests of GR as absolute minimum requirements (with multiple gravitational wave detections confirmed now, that is another test of GR that will become standard). You have been promoting your theory for a while but you haven't even started to meet these.

[SteveKelsey]

"There is a simple prerequisite in science for new theories: they have to be consistent with what we already know. "

Politely disagree.  There is a  prerequisite in science for new theories be consistent with the observed universe, nothing else.

[meberbs]

"There is a simple prerequisite in science for new theories: they have to be consistent with what we already know. "

Politely disagree.  There is a  prerequisite in science for new theories be consistent with the observed universe, nothing else.

I don't understand the point of disagreement. I thought context implied "things we know about the observed universe" rather than "things we know about politics," which clearly would be irrelevant. Meanwhile just saying "consistent with the observed universe"  seems like it would be too difficult to show, because there are things within our powers of observation that we don't "know" meaning that there is room for experimental uncertainty, or just that we don't know how to consistently combine certain experiments in any theory. The minimum should only be as good as current theories, not better, though you can't expect existing theories to be abandoned unless the new one is clearly better.

Do you have any issue with the specific examples I gave for this case? If not, then we are probably just using different words to communicate the same idea. I went with giving a specific example, rather than trying to precisely define what I meant by "know" in this context.