I’ll pick a couple low-hanging fruit. Well, it’s all low-hanging, but some is more exasperating than others.
This has been thoroughly answered. For my part, in posts 239, 243, and 247. Somehow you think it is appropriate to selectively profit from or ignore the gravitational field of the test object in order to prove your point. If you are going to include the gravitational field of your test object in your considerations, do it consistently!
Dude. You don’t seem to be thinking very hard about this. Atomic clocks are not affected by the earth’s gravitational field; only affected by the corresponding time dilation. Pendulum clocks are affected primarily by the earth’s gravitational field, and the time dilation effect is secondary. Just do the math (or learn the physics).
Mass increase is one way to interpret the non-newtonian formula for kinetic energy, but relativistic mass is only a useful concept in a limited way, and is therefore no longer used by most physicists. How about you stop arguing against something your opponents no longer use? The limiting factor is the kinetic energy.
How a particle is accelerated makes no difference, the fact is the kinetic energy, a relative phenomenon in Newtonian physics as well as in Relativity, follows a formula predicted by SR at high speeds (speed, not acceleration), not the newtonian formula.
You earlier argued against this by saying the speed in the rocket’s reference frame was zero, thus the kinetic energy is zero, showing a total lack of understanding of both Relativity and Newtonian relativity. The kinetic energy of a system is zero in its own reference frame in either. Kinetic energy is always relative.
The fact that you can’t see how ridiculous your “the rocket motor is part of the rocket”-argument is, speaks volumes.
I just stopped in here to see what this thread was about (since naita, so obligingly and succinctly answered my question in another thread), and now I think I shall slowly and quietly (well, not that quietly) back away and find myself another sandbox to play in.
You’ve also been asked to provide explanations to some experiments establishing the validity of special/general relativity within your framework. Your failure to even attempt to do so speaks volumes…
There’s also (still) the elephant of relativistic mass-energy equivalence in the room, which provides a lot of us with electricity, via nuclear reactors, or can be used as horrendously effective weaponry, whose efficiency is certainly well-documented (just try telling the Japanese you don’t believe it’s real…).
Again, you misunderstand the local nature of the equivalence principle. The lead and the piece of wood are not local wrt one another (they are in different places), so equivalence does not apply. Only the piece of lead, or a black hole, is of course easily explained: both in the case of a chest in a 1 g gravity field, or an accelerated chest, the gravity of the lead/black hole accelerates the bottom of the chest upwards, leading to the same local measurements in each case.
As I’ve said in my last post, the math that agrees best with experiment. Special relativity is able to explain all observed effects so far; you, on the other hand, continue to have to pick and choose in order to keep your preconceptions (‘particle accelerators don’t count!’).
The Michelson-Morley experiment has been carried out in vacuum, eliminating point 2. The de Sitter experiment rules out the possibility of the speed of light being referenced to the Earth’s gravitational field, eliminating point 3. Leaving point 4.
Max von Laue, using special relativity, predicted a positive result for the Sagnac experiment in 1911, two years before it was carried out (needless to say, the explanation did not involve any ‘universal frame of reference’; it was carried out in an arbitrary inertial frame, of course, since those are what special relativity deals with, but the analysis has been extended to, say, rotating and other non-inertial frames).
You continue to claim this, but fail to provide evidence to demonstrate the claim. In particular, it is still the case that the force that accelerates a rocket is not exerted by the motor on the rocket, but by the reactant on it, and thus, not ‘in’ any reference frame. No object can accelerate itself acting on itself; without throwing snowballs, the ice skater stays stationary.
Both the Fizeau and de Sitter experiments directly demonstrate relativistic velocity addition. Of course, so do particle accelerators routinely, but for whatever reason, those don’t count…
Because the limit that is being taken is m -> 0, which obviously is a hard limit for massive bodies.
Which one in particular haven’t they passed?
But this problem exists just as much in the Lorentzian theory as it does in the Einsteinian one – indeed, it was within the framework of Lorentz theory that length contraction was first postulated!
Though actually, it is even plain old electromagnetism that leads to such an effect. The electric field of a moving charge is different from the electric field of a stationary charge. In particular, if you have a spherical electric field, in a moving frame of reference, it will be ‘squashed’ – this is not arrived at by using special relativity, but by explicitly solving the Maxwell equations for the appropriate case. The calculation is a bitch, but was done by Oliver Heavyside. So, consider the electrical field of an atom, which determines how it is connected to other atoms in its vicinity. If in a frame in which it is at rest is spherical, it will be oblate in a moving frame. This means for, say, a measuring rod made out of such atoms, that in a moving frame, it will be shorter – concretely, physically shorter – because the distance between the atoms that make it up will be smaller in the direction of movement; in particular, this contraction will be different for different observers moving at different speeds. The amount of contraction arrived at this way exactly agrees with the special relativistic Lorentz-Fitzgerald contraction, such that today, one would use the Lorentz transformation to determine the electric field of a moving charge; but it can be done the other way around. So any theory, in order to be consistent with Maxwellian electrodynamics, needs to include length contraction.
So if you’re against length contraction, you’re not just against Einstein, but also, against Maxwell; and since you’re already against Newton, and against anything that happens in particle accelerators, you’re pretty much against the whole of physics.
If you look at something from a different angle, it will appear different for every given angle. How does the universe know what angle you’re at, to rotate the object for the correct amount? It doesn’t, and it doesn’t need to: the angle is given by the relationship between yourself and the object; similarly, the velocity is given by the relationship between yourself and whatever is length contracted.
And yes, the rotation is a real effect: the object’s length in a direction perpendicular to your viewing plane, respectively in a direction parallel to it, will in general change observably. In special relativity, it’s just that one of these directions is time, the other is length (and the geometry is hyperbolic).
The bent-stick is due to water’s effect on the propagation of light rays; the Lorentz contraction would be observable even if one could acquire instantaneous information about the contracted object. As has already been pointed out, there is an accompanying visual effect, Terrel rotation, which is due to the propagation of light rays; so a Lorentz contracted object would not merely appear contracted, but also, warped and rotated. If one corrects for those optical effects, what’s left is the contraction, which thus is not accounted for by optical effects.
Sure it would. Einstein assumes a time-varying gravitational field (it exists only ‘during the period of application of the brakes’), which thus induces a time-varying acceleration; but jerk is exactly what a time-varying acceleration is.
On time, as one can show for instance using Mößbauer interferometers in order to detect the (general) relativistic Doppler effect.
The man in the chest. I have changed nothing. This is exactly as Einstein wrote it. He said there was no way to tell the difference. I have pointed out there is. The logic is impeccable. Heavy objects fall faster. Of course the floor of the chest moves up as the heavy weight moves down, but by a tiny amount, unless using a miniature black hole the mass of the Earth in which case the movement is equal as the masses are equal. You are demonstrating that you have not read my web page which covers this point. The movement stops when the two collide, leaving the light object with some more distance to fall. Why did Einstein fail to mention this? The maths is done in my web page which you would know had you bothered to read it. The maths is actually for a black hole and a piece of wood or lead, just reduce the BH mass to something more manageable. The difference is there.
This is a classic piece of double talk from HMHW. “Again, you misunderstand the local nature of the equivalence principle. The lead and the piece of wood are not local wrt one another (they are in different places), so equivalence does not apply.”
As stated above, this is exactly as Einstein wrote it. Did he misunderstand his own thought experiment?
iamnotbatman wrote :- This has been thoroughly answered. For my part, in posts 239, 243, and 247. Somehow you think it is appropriate to selectively profit from or ignore the gravitational field of the test object in order to prove your point. If you are going to include the gravitational field of your test object in your considerations, do it consistently!
I have changed nothing. This is exactly as Einstein wrote it. He ignored the gravitational field of the test object, but I did not - read my postings again and do not mis-quote me.
“Max von Laue, using special relativity, predicted a positive result for the Sagnac experiment in 1911, two years before it was carried out (needless to say, the explanation did not involve any ‘universal frame of reference’; it was carried out in an arbitrary inertial frame, of course, since those are what special relativity deals with, but the analysis has been extended to, say, rotating and other non-inertial frames).”
The Sagnac Interferometer. Interesting that your link took me to the same page that I quoted from. This is not an SR answer. Note the formula used :-
t1 = 2piR / c (1-RwROT / c ) . The divisor is the speed of light modified by the rotational speed of the apparatus. In SR, the speed of light cannot be modified as it is the same for all observers (receivers). The “arbitrary inertial frame which the experiment was carried out in” was not the Sagnac Interferometer itself, it was the lab, therefore it was used as a reference for light speed, and it was a universal FR.
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A rocket with its own internal (reaction) motor can carry on accelerating as long as the fuel lasts. There is no motion between motor and rocket – ie they are both in the same FR, so there is no mass increase, and no other relativistic effects. To the contributor who said I did not understand Newton, look back at the postings using snowballs as an analogy, and the mass of the ejectant in a rocket motor. You will see that I do understand action and reaction. Perhaps my writing skills are poor, but it is plain what I mean.
“The Michelson-Morley experiment has been carried out in vacuum, eliminating point 2. The de Sitter experiment rules out the possibility of the speed of light being referenced to the Earth’s gravitational field, eliminating point 3. Leaving point 4.”
The MMX was carried out in the gravitational field of the Earth, so does not disprove point 3, as the starlight, on entering the local gravitational field, takes on the appropriate speed, much as it changes speed on entering water, glass etc.
How a particle is accelerated makes no difference, the fact is the kinetic energy, a relative phenomenon in Newtonian physics as well as in Relativity, follows a formula predicted by SR at high speeds (speed, not acceleration), not the newtonian formula.
“You earlier argued against this by saying the speed in the rocket’s reference frame was zero, thus the kinetic energy is zero, showing a total lack of understanding of both Relativity and Newtonian relativity. The kinetic energy of a system is zero in its own reference frame in either. Kinetic energy is always relative.”
That is exactly what I posted quite a while ago. The speed of the rocket in its own FR is zero, therefore the kinetic energy in its own frame is zero. That shows a total lack of understanding does it?
“So if you’re against length contraction, you’re not just against Einstein, but also, against Maxwell; and since you’re already against Newton, and against anything that happens in particle accelerators, you’re pretty much against the whole of physics.”
These attempted character assasinations are as ridiculous as they are purile. Somebody said I did not understand Newton, and the rest of you have jumped on the bandwagon. Your aim seems to be to throw as much mud as possible, and surely some will stick. I am certainly against Einstein, to use your phrase, but not against Newton, and what happens in a particle accelerator is correct, but the wrong interpretation has been given to it. PAs deal only with two FRs, and as said previously, if a force which is itself constrained to light speed, is used to accelerate (in this case) a particle, that particle can never reach or exceed the speed of the push force. This gives rise to the illusion of mass increase. (The particle cannot accelerate any more, no matter how much power we use, therefore its mass must have increased. From the Lorentz transformations, it then follows that time dilates and lengths shorten). All an illusion when looking from FR1 into FR2
This brings up the point of relativistic addition of velocities between FR1, FR2, and FR3 etc (as in the snowball throwing experiment). This has never been experimentally proved.
I was pointed to a web page which would prove me wrong. Of course it did no such thing – yet again. “Both the Fizeau and de Sitter experiments directly demonstrate relativistic velocity addition. Of course, so do particle accelerators routinely, but for whatever reason, those don’t count…”
Fizeau demonstrated the speed of light in water is different to that in air, and that its speed is WRT the water. The speed of light in the lab is always c ( or to be very precise c/n where n is the index of refraction of the air); in the water it is c/n (n now is the index of refraction of water. There are two FRs here, the lab and the water. De Sitter proved that the speed of light was independent of its source - nothing whatever to do with relativistic addition of velocities, and perfectly compatable with the local gravitational field theory. There are only two FRs here as well, the Earth and the star. Don’t bother nit-picking that as I know perfectly well that it is a binary star which is under discussion, but the argument is about the light from the less massive star on each side of its parent at different times in its orbit – hence only two FRs. Neither of these two experiments answer my query.
Particle accelerators are concerned with two FRs only. One with the accelerator in it, one with the particle in it. In these conditions, and these conditions alone, they are useful tools, but they have never shown the relativistic addition of velocities of particles with mass between more than two FRs.
What has never been proved is that a mass in FR1 which is at zero velocity WRT FR1 and is then accelerated by a force in FR1 to eg 0.9c WRT FR1 (the mass is now in FR2 at zero velocity WRT FR2), and then accelerated by a force in FR2 to a velocity of 0.9c WRT FR2 and is now in FR3, will still be slower than c according to an observer in FR1. Picture a linear particle accelerator which accelerates not just a particle, but another linear particle accelerator to 0.9c, which itself then accelerates a particle to 0.9c. That, or something equivalent, has never been done. The situation above describes the action of the rocket with its own internal rocket motor, so perhaps my writing skills are improving. The relativistic addition of velocities between more than two FRs has never been confirmed experimentally.
Einstein’s theories were not proved by the MMX, not proved by Fizeau, not proved by moving clocks as in the Hafele Keating experiment. There is no proof of the Lorentz transformations being applicable to more than two FRs. Einstein’s theories have not been disproved, but do not confuse no disproof with proof.
But of course it has. What you are describing happens routinely in particle accelerators. You accelerate a particle to near the speed of light. It is more massive than its decay products, so when it decays, its decay products are near the speed of light relative to it. Yet in the lab we never see anything faster than the speed of light. At the same time, all of the math hangs together. If you look at the situation from each frame, all the angles, velocities, lifetimes, work out consistently with the picture given by relativity. If you work it all out (a fun and simple exercise if you are up to it) you will see that nothing makes any sense or holds together at all if you try to insist anything other than relativistic velocity addition. I invite you to write it up like a homework assignment and put it on your web site.
Well, kinda they do, and kinda they don’t. Say NASA puts up two orbiting satellites. One masses 1,000 kg, and the other masses 2,000 kg. Well, they “fall” (orbit) exactly alike. The heavier object does not move into a different orbit. This is the same thing Galileo discovered, and is routinely illustrated by people dropping objects of varying mass from the top of the Leaning Tower (which, apparently, Galileo himself never did…)
In any case, you are altering the conditions and the purpose of the equivalence experiment. You could just as easily put a large electric charge on the object and on the floor of the chest, and watch them attract or repel. It isn’t relevant.
Arthur C. Clarke played the same game. He pointed out that gravitational attraction decreases with distance, and so a person in an elevator on a planet will feel just the tiniest bit lighter at the top of the elevator than at the bottom. True…and also irrelevant. In another trivial case, a person in a rotating space station (a la 2001: A Space Odyssey) would know this to be the situation because of Coriolis effects.
(Heck, one might just as well note that an elevator produces vibrations, and a box sitting on the surface of the earth does not!)
The point of the equivalence principle isn’t to deceive an observer who is equipped with sensitive instruments. It is to show that gravity “bends space” and thus produces acceleration, and that the two are indistinguishable intrinsically.
As Robert Sheckley said, don’t pick at the metaphor; it leaves a nasty scab.
I’ve never been able to figure out what you’re trying to say in this example. Okay, yeah, the motor and the rocket are connected. They’re usually bolted or welded together. The pilot, sitting up in front, is also in the same FR. So are all the stores, the fuel in the fuel tanks, and so on.
But as the rocket burns fuel, it uses the energy to eject reactant (burning exhaust, in ordinary rockets) backwards from the rocket nozzle. This mass, speeding backwards, shoves the rocket forward. The rocket and the reactant cease to be in the same inertial FR. They are now speeding apart and at remarkably high velocities. If the rocket goes fast enough, relativistic effects can be seen.
Alas, no, it is not at all plain. I don’t think I am alone here in saying…I do not know what you mean.
Again, what are you trying to say? Of course an object that is totally stationary has no kinetic energy with respect to its motionless self. But it has a lot of KE with respect to another, moving FR.
I’m sitting here, motionless, in my chair. Zero KE. And yet, because of the rotation of the earth, I’m moving at nearly 2,000 mph with regard to someone on the other side of the globe. If I were to use a Star Trek type teleportation system and go to the antipodes, I would arrive moving very fast, and would transfer a large amount of energy to the local environment. The damage would be astonishing!
And, again, this is merely Newtonian motion, having nothing to do with Einstein at all. It appears to me that you don’t understand this.
No… This has never been a personal vendetta or an attempt at character assassination. You are saying things that some of us think are wrong, and we are saying so. It’s our duty! We think we’re right, and we have at least a little evidence to back us up. You’re not stupid, and we’re not wicked. The issue is one of understanding and of communication.
It is demonstrated daily in every large particle accelerator on earth. It is demonstrated in satellites in orbit. It is demonstrated in probes orbiting Mars, Jupiter, Saturn, and flying free in distant space. Time dilation has been demonstrated with “atomic clocks.” Time dilation is also heavily implied by the existence, at the earth’s surface, of very short-lived isotopes, created in the upper atmosphere by cosmic ray impacts.
Exapno Mapcase: I’m participating for a number of reasons… To practice my science-writing skills; to practice my debating skills; to teach; and to learn! I’ve learned a lot from this thread! I’m definitely not in the league of some of the participants. In fact, I’m terribly trepidatious, as I know I am susceptible to error.
P.S. A friend of mine told me what your login name means! I fell all about laughing! Lovely!
You’ve taken a thought experiment about the equivalence between a constant gravitational field and constant acceleration and tried to put it in the real world where there’s no perfectly constant gravitational field. You have pointed out nothing of relevance to discussing relativity.
When brought up in a discussion of kinetic energy, yes, yes it does. The question here is: Newton’s laws gives us a formula for kinetic energy E = .5 * m *v^2 , Einstein’s relativity gives us one where E = (gamma - 1) mc^2. The latter can be shown to be equivalent within measurement error to the first at low speeds. The latter is experimentally verified. A competing theory has to logically lead to an equivalent or better formula for kinetic energy, and if it’s to refute the absolute speed limit of c, it has to not approach infinity at c like E= (gamma - 1) mc^2 does.
Newtonian and SR kinetic energy both being zero in an object’s own reference frame is not a relevant argument against this evidence for SR and the absolute speed limit of c. If you actually think it does, or there is some gem of insight hidden behind what to the rest of us appears to be an insistence on repeating that Newtonian and SR kinetic energy being zero in an object’s own reference frame is a refutation of SR, you need to communicate it better.
That’s not confusion, that’s how science works, even if the language may be inaccurate. All competing theories have been falsified by one or more of these experiments. Einstein’s theories are the only ones compatible with all the results. That makes Einstein’s relativity scientifically proven.
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As stated above, this is exactly as Einstein wrote it. Did he misunderstand his own thought experiment?
As Robert Sheckley said, don’t pick at the metaphor; it leaves a nasty scab.
Does that not apply to all my metaphors as well?
Trinopus Quote:
“. . . A rocket with its own internal (reaction)a motor can carry on accelerating as long as the fuel lasts. There is no motion between motor and rocket – ie they are both in the same FR, so there is no mass increase, and no other relativistic effects. . . .
I’ve never been able to figure out what you’re trying to say in this example. Okay, yeah, the motor and the rocket are connected. They’re usually bolted or welded together. The pilot, sitting up in front, is also in the same FR. So are all the stores, the fuel in the fuel tanks, and so on.
But as the rocket burns fuel, it uses the energy to eject reactant (burning exhaust, in ordinary rockets) backwards from the rocket nozzle. This mass, speeding backwards, shoves the rocket forward. The rocket and the reactant cease to be in the same inertial FR. They are now speeding apart and at remarkably high velocities. If the rocket goes fast enough, relativistic effects can be seen.”
This is why I clarified the issue in my last posting. Your sentence “The mass speeding backwards etc” is perfectly correct, as is the next sentence. The one after that though is totally wrong. They will never speed apart any faster than they did at ignition. The ejected mass is leaving the rocket nozzle at eg 1000Kph and accelerating the rocket forward at eg 10m/s^2 when the rocket is on the launch pad (or its starting point, which could be in orbit and therefore at orbital velocity. After any period of time ( I used that phrase to avoid referencing the rocket’s speed to its starting point), the mass leaving the nozzle is still at 1000 Kph, and not allowing for the reduction of the rocket’s mass due to the fuel being used, is still accelerating the rocket at 10m/s^2. This is what was meant by this paragraph :- A mass in FR1 which is at zero velocity WRT FR1 and is then accelerated by a force in FR1 to eg 0.9c WRT FR1 (the mass is now in FR2 at zero velocity WRT FR2), and then accelerated by a force in FR2 to a velocity of 0.9c WRT FR2 and is now in FR3… Picture a linear particle accelerator which accelerates not just a particle, but another linear particle accelerator to 0.9c, which itself then accelerates a particle to 0.9c.
The above paragraph describes the rocket motion in 3 stages. At each stage, the rocket is at zero velocity WRT the ejected mass. In fact it all happens as one fluid motion, due to the fact that the ejected mass is not ejected as one or two or three lumps or whatever, it is ejected as a continious stream of particles. It all becomes one smooth acceleration as the push from one particle is still happening when the push from another appears a fraction of a second later, and so on until the motor is powered down. At no point does the mass leaving the nozzle deviate from 1000 Kph (WRT the rocket), and at no point does the acceleration of the rocket deviate from 10 m/s^2 (WRT the mass ejected).
Trinopus Quote:
"Originally Posted by tomh4040
The man in the chest. I have changed nothing. This is exactly as Einstein wrote it. He said there was no way to tell the difference. I have pointed out there is. The logic is impeccable. Heavy objects fall faster. . . .
Well, kinda they do, and kinda they don’t. Say NASA puts up two orbiting satellites. One masses 1,000 kg, and the other masses 2,000 kg. Well, they “fall” (orbit) exactly alike. The heavier object does not move into a different orbit."
Actually appearances can be deceptive. Just as the man in the chest cannot detect a difference in the acceleration rates of the dropped objects (unless he has extremely sensitive instruments or uses exceptionally large masses, in which case he can), the 1,000 Kg satellite and the 2,000 Kg satellite appear to behave the same way in orbit because their mass is so tiny compared to that of the Earth. After a period of many years, and no I will not work it out, there will be a detectable difference in their orbits. To clarify this point, picture the miniature black hole the mass of the Earth in orbit starting alongside the 1,000 Kg satellite; they will very quickly depart from each other in different orbits. (And please don’t tell me that the Earth and the black hole will orbit their combined centre of mass, I know that). And if a mass of the black hole has a different orbit, then so does a mass half or a quarter or a tenth etc.
naita Quote: “You’ve taken a thought experiment about the equivalence between a constant gravitational field and constant acceleration and tried to put it in the real world where there’s no perfectly constant gravitational field. You have pointed out nothing of relevance to discussing relativity.”
As I keep saying, I have changed nothing, this is Einstein’s own thought experiment, so you are saying that Einstein pointed out nothing of relevance to discussing relativity.
Back to Trinopus “In any case, you are altering the conditions and the purpose of the equivalence experiment. You could just as easily put a large electric charge on the object and on the floor of the chest, and watch them attract or repel. It isn’t relevant.”
I know that is not relevant, which is why I have not said that. What is relevant is that heavy objects fall (accelerate) faster than light ones
Read Einstein’s man in chest experiment again. He does mention the Earth when talking about the gravitational field, with the implication of a 1G force, but you will find that he does not mention the acceleration used by the hypothetical being, and does not mention the value of the masses of the objects used. I am therefore free to pick any mass I like, and while using 1G acceleration as a reference, it is not strictly necessary.
Perhaps I accused iamnotbatman wrongly, but I have been mis-quoted by some contributors on this forum. Also thank you to Trinopus for remaining a gentleman, although I am suspicious when you say you still do not understand the point I am trying to make.
All very true. (Let’s assume no problem with refueling. Maybe it’s a ramscoop and fuels itself from interstellar hydrogen. No problem; it’s a simplified model.)
What’s happening is that velocities are added. But, from theory and observation, they don’t add arithmetically. They add using the Lorentz equation. So, the rocket (and, in fact, much of its ejected reactant) get closer and closer to the speed of light, but never reach it or surpass it.
I’m afraid I have to agree with naita and others: this is no longer the same idea that Einstein described. You’ve added a number of details, such as the black hole.
I think everyone here is making a superb effort at gentility. We’re all obviously frustrated, because we’re rather talking past one another. I’m certainly not feigning confusion; I’m honestly lost by some of what you have said.
All very true. (Let’s assume no problem with refueling. Maybe it’s a ramscoop and fuels itself from interstellar hydrogen. No problem; it’s a simplified model.) What’s happening is that velocities are added. But, from theory and observation, they don’t add arithmetically. They add using the Lorentz equation. So, the rocket (and, in fact, much of its ejected reactant) get closer and closer to the speed of light, but never reach it or surpass it.
Now we are getting closer together, but still have some way to go. As the thrust is always 1000 Kg, and the acceleration always 10m/s ^2, there is no increase in mass or any other relativistic effects on the rocket. What stops the rocket accelerating? I can stop the motor and coast for a while, in which case I become an IFR. Any experiment that I do will run exactly as it would in any other IFR (including measuring the speed of light). I start the motor again, and accelerate at 10 m/s^2 again. I can do this as many times as I want to. You can reference this back to any IFR you like, and sure the maths will tell you that you are traveling less than c, that is what the maths was designed to do. You say that this has been demonstrated by observation, but I am deeply suspicious of that statement.
iamnotbatman brought up this point :- “What you are describing happens routinely in particle accelerators. You accelerate a particle to near the speed of light. It is more massive than its decay products, so when it decays, its decay products are near the speed of light relative to it. Yet in the lab we never see anything faster than the speed of light.”
I am still in the process of looking that up. It is one of those soundbites which sound good until it is dissected. My first thoughts were, why use a particle which decays in a PA? If it decays in the PA, how is it in just the right place (where the detecting apparatus is) at the right point in its decay? If you are going to accelerate a particle to collide with a target, wouldn’t you want it to stay the course intact? I then moved on to a larger mass, plutonium to be exact, and started playing with that. That led me to this.
The plutonium is in the form of a cylinder being four times longer than its diameter, and it is subcritical. We will put this subcritical plutonium in a rocket with the length of the cylinder in the direction of flight, and fire it out into space. The rocket motor is very powerful and long lasting, and the rocket will eventually reach 0.9c WRT Earth. At this velocity, the length of the rocket and everything in it has contracted to 0.4 of its rest length. The plutonium goes supercritical and explodes, destroying the rocket. Now we will take a look from a different FR. This FR is an observer rocket which was launched at the same time as the plutonium rocket on the same trajectory, and is speeding away from us at 0.5c. The plutonium rocket’s velocity WRT the observer rocket is therefore 0.4c or thereabouts, and the plutonium does not contract enough to go critical. According to us on Earth, the rocket has exploded, according to observers in the other rocket it has not. If the rocket was programmed to cut its thrust at 0.95 c, the plutonium will never go critical and never explode. It can be recovered by the observer rocket. The plutonium rocket exists in one FR and does not exist in the other.
“I’m afraid I have to agree with naita and others: this is no longer the same idea that Einstein described. You’ve added a number of details, such as the black hole.”
The BH was there as a device to prove that a heavy object falls faster than a light object. By exaggerating the mass (using a BH), this fact was easier to prove psychologically. I will grant you that the difference is tiny, but it is there.
You are still displaying very basic misunderstandings of relativity.
The the case of the rocket example, the reason the acceleration is reduced in the lab frame (so that the rocket never exceeds c) is because as the rocket approaches c it is becoming more and more time dilated. From the point of view of the lab, the rocket propellant moves slower and slower as the dilation increases, and the rocket’s thrust gets smaller and smaller. Of course in the rocket’s own frame, it continues to happily accelerate.
In the case of the plutonium “paradox” you present, you have to realize that when the plutonium length-contracts so does the critical density needed for super criticality. All of the physical distance scales contract along with the plutonium; this is a very basic misunderstanding, and it shows how far you need to go before being able to remotely address any problems you perceive about special relativity competently.
In the case of the particle decays I mentioned in particle accelerators, there are many ways in which relativistic velocity addition is put on display. For one concrete example, consider when two protons are collided along the z direction. The protons have zero transverse momentum (momentum perpendicular to the beam line). The quarks inside the protons scatter off of each other, and are accelerated in the transverse direction from 0% to 99.9% the speed of light (for example). They often, for example, form charged pions, which you can watch travel for meters at 99.9% the speed through particle detectors before decaying. These pions are over 200x more massive than the electron + neutrino they can decay into, and in their own reference frame the electron produced from the decay is moving very close to the speed of light. But in the lab frame we watch the pion moving at 99.9% of the speed of light decay into an electron moving at something like 99.999% the speed of light. We can even go further. Sometimes the pion decays to a muon, which itself we can watch travel for meters before decaying into an electron. So we can watch a pion travel at 99.9% the speed of light decay to a muon which we watch travel at 99.99% the speed of light, which we watch decay to an electron at 99.999% the speed of light. (The percentages I quote above are not exact; I did no calculations, although I did have to do all of these calculations in college and then in graduate school. You get the idea)
Finally, the thing about the Einstein chest example and the equivalence principle. We have gone over this and even though the answer is completely obvious you just keep avoiding addressing it. Einstein was writing for a lay audience, and making a few basic assumptions which he may have not explicitly stated, but which are obvious to any physicist. We can debate Einstein’s ability to articulate relativity for a lay audience, but regardless you do not seem to understand the equivalence principle. Nothing you have presented is in any way in conflict with it. The problems with it you seem to have seem to stem from not knowing precisely what the equivalence principle is and how it is applied.
iamnotbatman quote “In the case of the particle decays I mentioned in particle accelerators, there are many ways in which relativistic velocity addition is put on display. For one concrete example, consider when two protons are collided along the z direction. The protons have zero transverse momentum (momentum perpendicular to the beam line). The quarks inside the protons scatter off of each other, and are accelerated in the transverse direction from 0% to 99.9% the speed of light (for example). They often, for example, form charged pions, which you can watch travel for meters at 99.9% the speed through particle detectors before decaying. These pions are over 200x more massive than the electron + neutrino they can decay into, and in their own reference frame the electron produced from the decay is moving very close to the speed of light. But in the lab frame we watch the pion moving at 99.9% of the speed of light decay into an electron moving at something like 99.999% the speed of light. We can even go further. Sometimes the pion decays to a muon, which itself we can watch travel for meters before decaying into an electron. So we can watch a pion travel at 99.9% the speed of light decay to a muon which we watch travel at 99.99% the speed of light, which we watch decay to an electron at 99.999% the speed of light.”
When I saw your reference to decay in particle accelerators, my memory was jogged a little. It is over 30 years since I did particle and particle accelerator theory, so I researched them again. I apologise for my gaffe.
In answer to your point about particle accelerators and the relativistic addition of velocities proving relativity, there is another scenario which fits. Let us assume that the velocity of light is WRT the local gravitational field, the medium it is passing through, or the (entrained) aether. All these three are near enough identical to each other for our purposes, just different names, so for ease of typing I will call it the aether. C is WRT the aether and the PA is also stationary WRT the aether, so c is WRT the PA also.
A simplified explanation of particle decay. The residual strong force holds the protons and neutrons of the nucleus together against the effects of the positive charge which is trying to repel them. If a proton finds itself outside the nucleus, this force is then unable to hold it, and it flies away from the nucleus by virtue of this repulsion. The repulsive force is an electric force and therefore operates at the speed of light, so the particle flies off near the speed of light. This last sentence is the important one.
As c is WRT the PA, when the quarks scatter, they are shot off at just less than c WRT the PA, not WRT the original protons. The same applies to the pions which are then formed, their speed is also WRT the PA. The electrons similarly formed also have a velocity which is WRT the PA. At each stage of decay, once the resultant sub particle has left its parent particle, it is on its own. It was pushed away in a once and only push from its parent, which must have been less than c. As c is WRT the PA, not the parent particle, it would follow that the velocity of the sub particle is not that much greater than that of its parent (this is from the parent’s FR of cource). Also it cannot undergo any more acceleration after leaving its parent. It is observed that these particles can never reach c. This is perfectly logical in aether theory. In the frame of the PA and therefore the observer, c is the speed of the pushing force applied to all these particles, therefore they cannot be pushed faster than the pushing force, and that is c in the PA.
You’ve got a lot of work to do, tomh4040. We accelerate the proton to near the speed of light using EM fields. Its speed in a particle accelerator has nothing to do with how fast it flies away from a nucleus. Besides, the protons are combed from hydrogen, whose nuclei consist of just a single proton. Furthermore, the fact that the electric field propagates at the speed of light has nothing to do with how fast the proton moves in reaction to the field (the strength of the field plays a role, for one thing). In any case I’ll stop you here. You have made so many mistakes in just a few sentences, there is no point in going further.
Quote from iamnot batman "You’ve got a lot of work to do, tomh4040. We accelerate the proton to near the speed of light using EM fields. Its speed in a particle accelerator has nothing to do with how fast it flies away from a nucleus. Besides, the protons are combed from hydrogen, whose nuclei consist of just a single proton. Furthermore, the fact that the electric field propagates at the speed of light has nothing to do with how fast the proton moves in reaction to the field (the strength of the field plays a role, for one thing). In any case I’ll stop you here. You have made so many mistakes in just a few sentences, there is no point in going further. "
The first paragraph offers an alternative view to relativity, and while you may not like it, it is a viable alternative. The second paragraph is almost a direct quote from Wikipedia, and though generic, and not specifically dealing with the hydrogen nucleus, the points made are very salient, especially the one about the protons and all sub particles being slower than light. The third paragraph simply states what is being observed in a PA, and puts a different explanation to it.
I drew your attention to the fact that these PA results can be explained by an (entrained) aether theory. That point has not been answered. The particle accelerator is supposed to be proof of relativity. It is not. The scenario I put forward shows that an entrained aether would give the same results as relativity. The MMX cannot distinguish betwen the two, nor can a particle accelerator. Please supply proof of where I am wrong.
