I know most of the answers will say infinity, but still this needs deeper look about its physical meaning and does it consider a practical logic?
Infinity usually used for something we could not measure, however the reality may be different!
The speed of light is defined to be 299 792 458 m/s.
* Please (i) calculate the energy E required to accelerate a mass of 1 kg to the speed of 299 792 457.99 m/s, and (ii) calculate how much mass M at rest you can create from that energy (by use of the formula M=E/c2).
* Estimate (i) the the total energy Esun released by the sun in one year, (ii) the mass Msun you can create from that energy, and (iii) the velocity v obtained by an electron if all that energy was used to accelerate it (assuming 100% efficiency, including no radiative losses).
* Estimate (i) the total energy within the "visible" part of the universe, and (ii) the velocity an electron would obtain if all that energy was used to accelerate it.
* Find the largest double precision floating point number which can be represented in your computer, and multiply the energy of the universe with that number. To which velocity could you accelerate the electron with the resulting amount of energy? Do you think it has gotten close enough to the speed of light?
The speed of light is defined to be 299 792 458 m/s.
* Please (i) calculate the energy E required to accelerate a mass of 1 kg to the speed of 299 792 457.99 m/s, and (ii) calculate how much mass M at rest you can create from that energy (by use of the formula M=E/c2).
* Estimate (i) the the total energy Esun released by the sun in one year, (ii) the mass Msun you can create from that energy, and (iii) the velocity v obtained by an electron if all that energy was used to accelerate it (assuming 100% efficiency, including no radiative losses).
* Estimate (i) the total energy within the "visible" part of the universe, and (ii) the velocity an electron would obtain if all that energy was used to accelerate it.
* Find the largest double precision floating point number which can be represented in your computer, and multiply the energy of the universe with that number. To which velocity could you accelerate the electron with the resulting amount of energy? Do you think it has gotten close enough to the speed of light?
Dear Kare
Thank you for mentioning these steps. This suggests a real modification required to the energy mass equation at the velocities very close to speed of light.
Sadeem> This suggests a real modification required to the energy mass equation at the velocities very close to speed of light.
Why? In a Lorentz invariant theory there is always an inertial frame where the particle is at rest...
Dear Sadeem,
it may sound trivial - but the rest mass remains the same anyway. The notion of a changing mass is missleading and apparently most researchers in this field have abandoned it. See e.g. " Energy and Mass in Relativity Theory" by Okun.
the question is: "If a non zero rest mass object is moved at speed of light ..." It doesn't say: is accelerated till the speed of light. So: how to transfer a massive object onto the light cone? by bringing together a particle-antiparticle pair, like electron/positron. Now observe, pair creation and pair destruction is a noncovariant concept. In other words, we really doen't know, how to pass on or off the light cone. It seems too simple, but the best answer could be: a kind of restmass of the photon is hn/c2
Dear all
Worthy answers, but little different from each other.
Some of the answers stated that massive particles couldn't reach speed of light,
I agree with that but still the energy for such particles is important to be known at speed of light at least theoretically because it may lead to an interpretation or give some hint about some phenomena that occur for high energy particles.
Other answers stated that there is a need to a correction for the transformations, which I also agree with
other ones stated it may be related to rest mass of the photon, may be why not...
So the question is still opened
Thank you
Another way to look at this problem is to see how the electron accelerators work; in which a bunch of electrons are accelerated to nearly 99.98% of the velocity of light. As these electrons are being accelerated in circular path therefore they lose energy at the tangent point of their orbit. However, the conversion of mass into energy definitely follow e=mc2 relation which is a practical demonstration of accelerating a non zero rest mass particles to nearly the velocity of light.
Aslam
This question was actually discussed very seriously a few years ago. It could be that the maximum allowed speed of massive particles is a little larger than the speed of light. That is an obscene thing to contemplate, but it does happen in water. Perhaps it happens in what we perceive to be a Lorentz invariant vacuum? Then the energy of the massive particle with the speed of light would very likely be finite. But the particle would be on the brink of emitting Cherenkov radiation. In connection with the (wrong) Opera results, Glashow computed that faster-than-light neutrinos (although over-all neutral) would emit Cherenkov radiation.
Today I am doubly happy. Some serious scientist begins to think in some situation the speed of massive particles can be larger than the speed of light. Perhaps it is time for beginning a serious discussion.
STR does not allow a massive body to dynamically-acquire (i.e. through acceleration) speed of light.
I have understood, but I am a researcher and old theories are useful in order to go ahead.
caro Dottore Daniele, me too, I'm so happy to learn, that italian physicists still process Eredidato's most famous neutrinos "faster than light". Just go ahead, those neutrinos you'll get from CERN!
caro Dottore Anton, my research on neutrinos is very clear: neutrinos are energy particles and they move exactly with the speed of light. The physical speed of neutrinos cannot exceed the speed of light.
Besides I not would understimate the meaning of the CERN experiment. Despite the mistake (i.e. neutrinos were faster than light) that experiment was useful in order to understand better the behaviour of neutrinos.
"that experiment was useful in order to understand better the behaviour of" ... SO CALLED CERN EXPERTS like Eredidato, who had to resign, or did you forget this?
I think it is interesting to contemplate Sadeem's question in light of certain hypotheses, such as those of Asif and Zampino (Asif has been accepted by EPJ by the way) in which matter is essentially just electromagnetic radiation propagating in some odd way .. we can visualize it as circular though it may be more complex. These theories solve the problem of charge confinement which plagued earlier all-EM theories of Poincare and Lorentz, and nicely explain the easy conversion of matter to and from EM radiation. There are many things they as yet do not answer, of course.
But in this model, you see that as long as the light is circulating, you can get a higher and higher percentage circulating in the direction of propagation, but not all of it.
Another thought is that if you had a (very hypothetical) system for annihilating matter into EM radiation and preserving its state, and a complementary system for restoring it, then a particle of mass m so-represented by the EM radiation would have a minimum theoretical mass limit of something like 2m (to account for the necessary antiparticle), plus extra for redundancy and communication losses.
Dear Sadeem,
It is interesting to review the experiment performed by Bjorken which was supported in second instance by Richard Feynman who was enthusiastic when he learned about it. This was put in place in order to probe the existance of the components in the nucleons structures which at first were classified by partons and then by Quarks by Murray Gellman.
The very high powerful electrons used in the experiment had so small radii that they could enter the inner structure of the proton in a deep inelastic scattering and make an adron radiography in the same way it was performed for atoms at the beginning of 1900 by Rutherford (with the nuclides against the very thin gold slab).
The maximum speed that an electron can reach is the one which gives it the maximum possible energy and minimum lenght and that is the Planck energy
Ep= sqrt(hc5/G) = 10^28 eV. This should push it at the maximum possible speed in this universe which is supposed to be the limit for this hyperspace or background which allows these laws of physics to take place. This should correspond to the closest velocity to the speed of ligth possible, since after that it would be unfeasible to further provide any energy to the particle because it would become a black hole and this would correspond to the Planck mass.
"at first were classified by partons and then by Quarks by Murray Gellman."
these "partons" were truly obscure objects, just a scale property, and not comparable with Rutherford's experiments. Proton-electron collisions have to reveal clearly the masses of quarks and this never happened till today. They may be confined, but they have to be visible in scattering experiments of Rutherford type.
Stefano> the experiment performed by Bjorken
Just some historical corrections. The (SLAC-MIT) experiment was not done by Bjorken, but by a different group of people; three of these received the 1990 Nobel Prize in Physics. They discovered some surprising behavior of high-energy (high at that time) electrons scattered on nucleons.
To my knowledge the theoretical physicist James Bjorken gave a phenomenological description of the results, to be called Bjorken scaling. The main feature of the results was data collapse: A function which generally should depend on two variables actually depended only on one special combination of them (somewhat crudely speaking). I don't think Bjorken constructed a physical model explaining this behavior. Feynman did, by showing that the results would come out naturally if protons and neutrons were composed of smaller entities, which he called partons. I don't know why he didn't want to associate these entities with quarks (which had been invented earlier by his colleague Gell-Mann in their common corridor at Caltech). There was some years of discussion about how the experiments should be interpreted (that partons where obscure objects etc, as mentioned by Anton); for all rational people this ended in favor of quarks in november 1974 (it was embarrassing to hear Schwinger continue to push the long dead alternative much later).
The final answer is that there is a substructure of nucleons, similar to the discovery of Rutherford for atoms. But not as pronounced, and with much more subtile and interesting behavior, which has been important for the development and verification of QCD.
http://www.nobelprize.org/nobel_prizes/physics/laureates/1990/press.html
Sorry to Sadeem, for diverting extremely far from his topic in the above post.
To return to his topic. Even though an electron can have an impossible-to-understand amount of kinetic energy, as viewed from one frame (as I have tried to dramatize in an earlier post), this does not-at-all mean that it has to create a black hole. There is another frame where the electron is at rest with its normal energy, just like all electrons in and around us. To consider the creation of black holes, one must not only consider the energy but also the momentum. It would be a different matter if we collided two almost-infinite energy electrons moving in opposite directions.
Anton> they have to be visible in scattering experiments of Rutherford type.
Parton distribution functions have been measured, and are published by the Particle Data Group.
http://pdg.lbl.gov/2015/reviews/rpp2014-rev-structure-function-figs.pdf
Stefano suggests on the previous page that an electron accelerated to greater than a certain limiting amount he supposes would become a black hole. We might learn something from this. It is not necessary to limit it to an electron. It could be anything.
Can you make something a black hole by accelerating it? I'm doubtful. I think it would have to be a black hole in its own rest frame, or else it's not black. If something could escape in the rest frame where it still has only its rest mass, then it's not black.
We could start with a large object, say a neutron star, which would only have to get to a few percent of c to have the requisite mass. What then?
If you think this is a black hole, then I say that aliens, or even a particle, traveling through our solar system, would view the sun as traveling sufficiently fast to become a black hole, and the solar system would collapse. We get cosmic rays all the time, but it doesn't happen.
What does this have to do with masses traveling faster than light? Well, a black hole is already traveling at the speed of light in its own rest frame, if you use Schwarzschild coordinates instead of local proper measure (which is meaningless anyway). Because the coordinate velocity of light at the event horizon is zero.
But black holes can and do move. They respond like any mass in an orbit, and I'd bet pretty much anything they respond in the normal way to momentum collisions with other large objects.
But these other large objects can never reach the event horizon? Or can they? Perhaps the presence of gravity on both sides of the horizon opens it up? Klaus was pointing out that numerical calculations of things like merging black holes are done routinely, but he couldn't describe it. I'd like someone to try, and explain how things move faster than light and move a black hole, or how the supposedly inviolate event horizon opens up. Either outcome sounds interesting.
Stefano's hypothesis that "an accelerated electron to greater speeds than a certain limiting quantity can become a small black hole" doesn't have meaning in the gravitational theory of black holes, but it has a realistic meaning in the order of the relativistic theory of black holes.
@Kåre Olaussen : distribution function? we need Rutherford-like CROSS SECTIONS, what else? Tell, me, why will these "quarks" not follow plain simple rules of physics and show their cross section by high energy p,e scattering?
Anton> why will these "quarks" not follow plain simple rules of physics
In my opinion they do, just like electrons bound to an atomic nucleus do.
The rules are the same, but the details are different. Most important because αs is much larger than α, which f.i. makes the amplitude for a virtual gluon transforming to a quark-antiquark pair much larger than a virtual photon doing it. I think you can (and perhaps should) apply the Altarelli-Parisi equations to the electron distribution functions of atoms just like they are applied in deep inelastic scattering. The initial distribution is of course different, and its evolution much-much smaller (probably observationally negligible). The fact that colored particles are confined does not seem to play much role in the theory of deep inelastic scattering.
dear Kare, are you serious? I have to change only some parameters in Rutherford's cross section formula and I'll get a rough estimation of these quark masses!!! The fact, that this never happened and NEVER will happen shows, that these "quarks" may - till today - be considered as some auxiliary fields for a preliminary understanding of "strong" forces . The well known fact, that the overwhelming majority of physicists "BELIEVE" in quarks sheds only some light on the miserable today state of elementary particle physics.
I think the confusion is because one is confusing between what is called as the rest mass and mass of a moving particle. Strictly speaking, it does not make sense to talk of mass of a moving particle. Rest mass is the property of the particle and it should be identified as the mass of a particle/object. A moving particle has energy and momentum which are related by equation E^2 = p^2 c^2 + m^2 c^4. There is also a relation between energy, momentum and velocity of a particle. The relation is p/E = v/c. This follows from special relativistic relations.
A moving particle can be considered to be stationary in a reference frame moving with the velocity of the particle with respect to observer's frame. In this frame, the particle is stationary. If a particle of nonzero rest frame moves with velocity of light, that means there exists a frame moving with velocity of light (w.r. t. another frame). These two frames must be related by a Lorentz transformation. But Lorentz transformation rules show that this is impossibility. So, a massive particle cannot move with velocity of light. Conversely, a particle moving with velocity of light (photons or neutrinos) must be massless.
It is best not to think of change in mass of a moving particle. Mass of a particle is defined in its rest frame and does not depend on particle's velocity. It is invariant. What changes is its energy and momentum.
Dear Phatak
Or
Because Lorentz trasformations are not valid at speed of light, aren't they?
I disagree with the fashionable but misleading statements that "...it does not make sense to talk of mass of a moving particle". Motion does not deprive an object of its mass, it only changes its numerical value. This is an experimentally established fact which cannot be denied or just ignored by a physicist. See, e.g., Kaufmann- Bucherer - Neumann experiments which had showed the dependence of the inertial mass of electrons from their speed as far back as 1901-1915. In order for this type of discussion to make sense, it is necessary to define first the the concept of mass. Actually, we have two definitions of mass: as a measure of the amount of matter in a body, and as a measure of body's inertia. The first can be measured, for instance, by weighing the body, and the second is determined as a ratio of the applied force to the resulting acceleration. Both definitions go peacefully together in the non-relativistic limit. But generally, they represent two different characteristics with different behavior. The first definition - mass as the amount of matter in the body - applies directly to the body at rest. It tells us what we get if we stop the body, and is represented by a constant m0 - the rest mass. For instance, if we try to stop a photon in an empty space, we get nothing, which means that the photon's rest mass is zero. But we do not actually need to stop a moving object or to catch up with it to measure its rest mass - we can instead measure its energy E and momentum p and find m0 as the invariant m0= sqrt{E^2-(pc)^2}/c^2. If we apply this procedure to a photon, we will get zero. The second definition - mass as the amount of body's inertia (call it inertial mass) is more subtle because in the relativistic domain, acceleration is generally not parallel to the applied force. The conventional definition of the inertial (relativistic) mass m(v)=gamma(v) m0 (with gamma(v)) being the Lorentz-factor) is the ratio of the force to acceleration when the force is perpendicular to v. The concept of relativistic mass and its applications are described in details in my book "Special Relativity and How It Works", Ch. 5 and 7. You can also find the relevant discussion in "Three +1 Faces of Invariance", arXiv:1001.0088 [physics.gen-ph].
Anton> The well known fact, that the overwhelming majority of physicists "BELIEVE" in quarks sheds only some light on the miserable today state of elementary particle physics.
I used to hear such skeptical statements about quarks before November 1974.
The discovery of charm, and later the bottom and top quarks, have convinced most people of the existence of quarks. It is the totality of measurements in combination with quantitative theoretical explanations (consistent between phenomena), which build the case.
Deep inelastic scattering at a single (high) energy can only be used to fit distribution functions. But this knowledge, in combination with theoretical predictions of how these distribution functions change with scale, can be used to predict the results of scattering at higher energies. The available accuracy of the predictions is not always fantastic, but altogether deep inelastic scattering makes a very strong case for the existence of quarks, gluons, and the theory of Quantum Chromodynamics.
Another independent phenomenon is the observation of hadronic jets in electron-positron annihilations, and the properties of these jets compared with theoretical calculations.
The explanations for hadronic spectroscopy and other static properties. The explanation for the lifetime of the neutral pion. The consistency of the Standard Model, with the verified prediction of the top quark (actually, charm had also been predicted before it was found).
Altogether it is not a question of belief.
Moses> I disagree with the fashionable but misleading statements that...
I think you belong to a diminishing species.
It is not that I think anything you say is wrong. It is only a matter of wordings. We don't need a special word for the description of E/c2. And the concepts of longitudinal and transverse inertial masses only adds confusion and mess to a beautiful and elegant field of science.
https://www.researchgate.net/post/What_are_the_worse_yet_enduring_misconceptions_about_mass_and_energy_in_special_relativity
Sadeem> Lorentz transformations are not valid at speed of light
Yes, they are (as far as we know). In fact, the symmetry group for massless particles (or the source-free Maxwells equations) does not only consist of the 4 translations in time and space, and the 6 Lorentz transformations (which forms the 10-parameter group of Poincare transformations); it extends to the 15-parameter group of conformal transformation, by adding one scale transformation and four special conformal transformations to the symmetries.
There's no possible way this question can be addressed as stated-it doesn't make sense. The definition of mass relies on Lorentz invariance, otherwise it's not well-defined. And there isn't any frame, obtained by a Lorentz transformation, in which a massive particle moves at a speed equal or greater than the speed of light in vacuum. It is, however, possible for an object, in a medium, to move at a speed greater than the speed of light in that medium-which is less than the speed of light in vacuum-and then the result is known: it emits radiation, called Cerenkov radiation.
The Lorentz Transformation states that there is a singularity at the speed of light. Mass moving at any velocity is a function of its velocity, it's not a constant. The Lorentz Transformation says that the mass blows up at c, which means the energy needed to accelerate such a mass also blows up.
E = mc2 describes the total intrinsic energy of a mass at rest, if that mass is entirely converted into energy.
So I don't see any inconsistency here. Take a mass at rest, convert it completely to energy, and the energy is still not enough to accelerate that mass to v = c.
As to the Lorentz Transformation, who knows. As of now, unless I missed some astronomically important news item, it's still valid. But one never knows. We used to think that classical physics was correct, only to discover that classical physics gives a good explanation only at lower speeds. Perhaps relativity also breaks down eventually. But it's not right to dismiss relativity outright, every bit as much as you can't dismiss classical physics outright. You simply need to define the limits of its applicability, when/as/if those limits are determined..
Dear Kare
I think at speed of light all these trasformations are not valid anymore, unless one adds the terms that considers the violation of CPT as done in certain works that intend to interpret an anomoulus factor that found in gamma factor during high energy experiments.
Dear Sadeem Fadhil: "If a non zero rest mass object is moved at speed of light how much its mass should be appeared?"
Let's analyse it the physical way, even if this will bother proponents of the relativity theory. Take a supersonic bang. In theory, it is infinite as well, but in reality, the sound is just very hard. The reason is that the emitted sound energy at the bang can not be more than the accumulated sound that has been obtained before the bang. And the jet has enough power to accelerate fast to that point.
Why wouldn't fast particles not become superluminal? The problem is: what kind of process will get them that fast, and moreover, without desintegrating them? The accelerators don't have tools that can do that, because they use electromagnetic fields that are limited by the speed of light themselves.
If however a particle would become superluminal with a new kind of succesful process, it would only emit the energy that has been accumulated during the accelerating process, including its own energy if it desintegrates, not more. Like with a supersonic bang.
Returning to the initial question, in the order of Special Relativity mass of any massive object tends to infinite when its speed tends to the speed of light.
In the order of the Theory of Reference Frames there are two answers according as we consider ordinary objetcs or elementary particles.For ordinary objects inertial or gravitational mass is independent of the speed and therefore it is constant with the speed. For elementary particles electrodynamic mass, considered at rest, decreases with the speed and it is the half at the speed of light and zero at the critical speed. I am available for explanations with regard to the Theory of Reference Frames.
It needs to specify what theory of relativity one is considering.
Sadeem> an anomoulus factor that found in gamma factor during high energy experiments
Please give a reference to what you are talking about.
In special relativity, the only way to define the mass of an object implies that it is invariant under Lorentz transformations-so it doesn't depend on the inertial frame. While it is, of course, possible to multiply this quantity by factors that do depend on the frame, the fact that they do means that they don't have any physical meaning-they're coordinate artifacts. It doesn't make sense to argue over the meaning of quantities that can't be assigned any.
Dear Kare
Take as an example these references,
http://arxiv.org/pdf/0905.4346.pdf
http://arxiv.org/pdf/hep-th/0507258.pdf
http://arxiv.org/pdf/hep-th/0609030.pdf
With best regards
When nature shows strange behaviours and violations of some fundamental concepts of a theory, it is possible to proceed to the correction of those violations through procedures ad hoc, renormalizations, reparameterizations, additions of corrective terms, etc.. . This road leads normally to the complication of initial physico-mathematical models and to the situation in which a correction in one point of the theory produces failures in another point: the result is a puzzle that demolishes the initial structure of a theory and it doesn't reach an acceptable new theory. In these situations it is suitable the research of new physico-mathematical models.
Sadeem> I think at speed of light all these trasformations are not valid anymore, unless one adds the terms that considers the violation of CPT as done in certain works that intend to interpret an anomoulus factor that found in gamma factor during high energy experiments.
I only skimmed the most recent of the papers you linked to. It clearly says that nothing was found! And the experimental bounds (experiments can only provide bounds -- always) are quite stringent.
I understand you have some fancy for modifying special relativity at high energies, or velocities close to c. Nothing wrong with that, but you cannot motivate such attempt by existing experimental results.
Dear Kare
Of course one doesn't expect a large anomalous factor, don't forget we are dealing with velocities that are still below the speed of light when we reach closer velocities we may get even more deviation from Lorentz factor. So, still we can't assume the applicability of traditional Lorentz transformations at speed of light, because these papers contain experimental results that indicate such deviation from them.
Sadeem> because these papers contain experimental results that indicate such deviation from them.
I don't understand at all how you can interpret the linked papers the way you do -- they contain no experimental results that indicate any deviation. If any such results, from serious experiments, had existed, this would have been discussed all over the place.
These papers contain experimental results that provide bounds for the deviations. And the point is that the deviations are consistent with zero. Any experimental result provides bounds, the question is whether the deviations are significant-and it turns out that they aren't.
the results from LEP experiment from the 1st ref.
"The energetics of the LEP beams were extremely well understood,
and measurements of the synchrotron emission rate indicate that the isotropic Lorentz
violation coefficient......."
"The electromagnetic sector behaves according to
ordinary special relativity, except with a modified Lorentz factor ˜γ = (1 − 2*κtr − v^2)^−1/2"
I don't know do you see the additional factor (Ktr) in traditional Lorentz factor!
if the world doesn't want to admit it, this is another issue, but these are experimental results indeed and you can check it from the website
please note that c is assumed one in the above equation
One shouldn't cut and paste isolated phrases. These variables parametrize possible ways to describe violations of Lorentz invariance-what matters is the additional term can be found to have a value consistent with zero.
Dear Stam
These variables are the summary of the analysis of experimental data and the violation is real as assumed by the paper (just read it) and you can easily reach this conclusion, the paper only wants to give the limit of this violation factor
A ``violation factor'' doesn't have a limit-it has a value. This value can be bounded by experiment and the only interesting issue is whether the bound is consistent with the statement that the value is zero-or not. Since the bounds are consistent with the value being zero, this means that any non-zero value is an artifact of the experiment and doesn't describe the physics.
You are looking to it from the view of classical SR, while the paper state it in the frame of CPT violation theories, "Presently, there is quite a bit of interest in the possibility that Lorentz and CPT may not be exact symmetries of nature. If the laws of physics, in their most fundamental form at high energies (e.g. at the Planck scale), do not respect these symmetries, then there should be evidence (however weak) of that fact at observable energies. There would be Lorentz- and CPT-violating effects in the effective theory governing low-energy phenomena."
Please don't underestimate the no. even if its 10^-15, don't forget we are talking about elementary particles at extreme velocities not about GR dimensions, so even small violation matters
Lorentz violation implies CPT violation-the question is what way is easier to search for them. Once more, this bound is consistent with zero-one should read the whole paper, not just the abstract. Violations or any effects matter if they're significant, not if they're not. These measurements are interesting because in this way they can control background. They now know that, if they find any *other* deviation, whether it's background or signal.
There are another evidences from astrophysical data which also support the conclusion of the violation, so its not a unique evidence
Of course not-once more, one shouldn't confuse intervals with vales; that a quantity is measured to have a value within a certain interval doesn't mean that all values within that interval are distinguishable. Also, that violations that are claimed in one experiment must explain why similar violations don't show up in other experiments.
Sadeem, you have a strange way of reading and interpreting scientific papers. I am afraid you will have great problems with referees and editors in the future, if you continue with this practice. And that would not be because anyone tries to suppress your ideas and work, but because you base your conclusions on serious misunderstandings.
> Stam"Also, that violations that are claimed in one experiment must explain why similar violations don't show up in other experiments."
Simply because these effects are related to extreme velocities close to c, we only have it on earth artificially through the LEP experiment. Even LHC experiment can't show it because the velocities of hadrons are not as its for electrons unless we reached to extreme energies that make these particles reach such velocities. The other source is from astrophysical data which contains even more energies than the LEP.
> Kare
lets leave my problem with the editors for a while and give me something scientific to talk about
In coventional textbook versions of SR the answer is: the mass is infinity
m= m0/ sqrt(1- v^2/c^2).
That is why no one has got a particle up to the speed of light
PS You will always get someone who likes to change things around.
We know that you can't accelerate any object to the speed of light.
If we wanted to discuss on the reason of this, we could use Lorentz factor, as Andrew has written, but Lorentz factor itself (and Einstein himself) consider the limit at "c" as a matter of fact (the factor is mathematically structured to have the speed of light as an asymptote), with no quantum explanation. The theory of relativity needs this (unexplained) assumption: nothing can move faster than light and nor at light's speed.
Let's try to go a bit further, after one century.
If you consider an object moving through vacuum space at a given speed it's not moving through a real vacuum but through quantum vacuum, which is only a step back to be considered a (fluid) quantum space. In my work I consider that quantum space is superfluid and - just as all superfluids - it has no real zero viscosity.
Thus, it would occur that its minimal viscosity produces an effect of dilatancy (apparent viscosity) when shear stress is driven to relativistic velocities (as in the case of an accelerated object). Since - as an answer to the linear increase of velocity (acceleration) dilatant fluids show a non linear increase of viscosity (as an apparent force opposite to motion) you get an asymptote. In a few words, from the point of view of fluid quantum space, accelerating a body to the speed of light is like accelerating it through a wall. Impossible. The properties of quantum space don't allow that. Moreover time (clocks) would be stopped in the accelerated frame of reference blocking acceleration.
Of course this is still an unconventional approach to this issue but where no thorough answers are available, it deserves to discuss.
Article A superfluid Theory of Everything? [outdated version]
It is well known that a motion of an object with friction reaches usually a final sped. A quantum vacuum is never a "fluid" and a quantum state is never a massive object. Next, a "state of a massive particle" has a reference frame where this object is AT REST! Now, it's ME, the observer, who sits in a reference system which moves against the rest system of this particle. From MY point of view this particle may move, however, the particle itself did not move a bit. In this scenario this fluid around the particle is still at rest, nothing happens.
What you did is a revival of the ether theory, pre-Einsteinian physics. I assume you are not impressed from these arguments.
Anton, it reaches a final speed if acceleration is not increased. An object falling in in the atmosphere reaches a final speed but if you attach to it a sort of propeller then it can move faster. As supersonic airplanes move faster than sound. Air is not dilatant, it is a newtonian fluid. In a dilatant fluid things are very different.
About quantum vacuum we're allowed to call it quantum space (since it is everywhere) and there are two ways of describing it as a quantum structure: 1) it gets a quantum nature only in the moment electron-positron pairs stochastically pop here and there.
2) it is composed (always and everywhere, not stochastically) by space's quanta. In this case it can be described as a fluid, why not. Of course not a fluid of matter (no atoms or molecules) but a fundamental quantum energy "scalar field" (zero point field), probably the most elementary, beneath Higgs field. I'm not the first to speak of a fluid quantum space.
The frame of reference of a massive particle is "at rest" only if the particle is in equilibrium (i.e. stationary or moving at constant translational velocity or with constant acceleration > equivalence principle). If acceleration changes it's not at rest in its frame. And if you consider a perfect reciprocity in the point of view the paradox remains unsolved. You know that specialists in relativity use a third virtual observer to solve the paradox.
Finally, about the pre-einsteinian physics (I think you refer to the issue of an aether and the Michelson-Morley experiment) if you want you only need to read my paper first, because it exactly discusses also that issue, by pointing out that - in this case - it's totally different. The MM experiment considered that Earth was moving through an aether, while I say Earth (fermions) is absorbing space's quanta. The flow is then directed downward, toward Earth center and corresponds to the gravitational field, matching Einstein's predictions (red/blueshift) and other. We know that science is often made of subtle differences which make a great difference.
Hi Marco, "it is composed (always and everywhere, not stochastically) by space's quanta." only in your mind!
ähem, how bout time quanta?
If a mechanical system with inertial or gravitational mass mo moves under the action of a force F into a real medium with friction coefficient k, the final speed is F/k. Increasing F or decreasing k the speed increases. Dynamics put no limit to the speed of motion, limits in present physics come from kinematic considerations. For electrodynamic systems things are actually different because electrodynamic mass of elementary particles, for instance electron, is certainly different from inertial mass of mechanical systems: I think nobody can suppose that an apple, for example, and an electron have the same type of mass.
@Anton,
you surely know loop quantum gravity (Rovelli), and other theories of quantum gravity which deal with a quantization of space. I'm not the first who speak about such a concept. You want to give me that honour, thank you, but it's not so.
Moreover, if you suppose that space is quantized and you think of GR's tidal forces as space's quanta absorption effected by matter, the mathematical model perfectly functions. In my CFD simulations Newton's law has indeed been obtained. That's mathematics. And still through mathematics I show that the whole theory of relativity (SR and GR) can be explained and included (and simplified, this is important) as a mere function of gravity (explained that way, through a quantization of space).
So, when a model explains and simplifies a lot of things it's worth to be furtherly discussed, analyzed and verified.
From your reasoning you should write to the guys who wrote string theory and tell them "that's only in your mind", and also to those speaking of gravitons, and also Einstein's relativity was only in his mind (and in mathematics, again) before experimetal confirmation.
Many people has a own theory and the difference is made by the fact that some may (or not) function in computer simulations and in the mathematics, such as mine. If so, we pass to experimental verifications. Otherwise it's only "in their minds", right.
@Anton
Let's consider E=mc2 , let's put m=1kg and let's focus on c2. It is a square distance (dimensionally m2/s2) but we could also see c2 as the area defined by light in one second (a square whose side is 3*108 m). Let us imagine this area corresponds to a layer of space's quanta. In this way we could calculate the energy of the layer, of a cubic portion of space with side 3*108 m and of 1 m3 , which would correspond to 1 joule. Then divide 1m3 in small portions of cubic Planck's lengths and give each of it the corresponding energy.
@Marco:
The universe goes SI!!!
1m³ “space” contains 1 J energy!
You wrote this under: 1)
This cube is now filled up with your SQ’s.
Filling a fixed volume with objects what so ever is not quantize the space.
So far my privat library is quantized by my books.
The concept of Anton's quantized library seems to me very beautiful and at the same time effective and useful. Similarly we can think a quantized physical space into the mathematical structure of the continuum space. Let us obtain like this a model of " discrete space into the continuum".
Sadeem,
My guess is that your true question is "can we hope, somedays, to visit the stars ?" . I have posted this question on this site, and received very few answers from the academic public (who does not seem interested), and some others very interesting, that you will not find on arXiv.
I agree with Daniele. Anton's metaphor of quantized library is okay to describe quantum space. Indeed, we can speak of light's quanta (photons) which can be emitted, can travel, can scatter... but if a quantum space exists it has to be everywhere all the time. Just like a library (normally) doesn't travel and it's not produced or absorbed here and there. But the most useful comparison about fluid quantum space, is the ocean. We could say its "quanta" are all water's molecules which form it (just to make the comparison).
And ocean's currents are like the gravitational flows I describe in my work. I and the engineers who worked with me have shown that Newton's law of universal gravitation perfectly works in this way. And also SR's and GR's effects work on a fluid dynamic basis. So, it's worth to furtherly investigate this issue. Just that.
Also, about this comparison, let's imagine to have a hole on the ocean's floor. It would create attracting currents just like a mass produces gravity.
And I add a detail to my previous post above:
by considering c^2 as the energy of 1kg mass (and 1 kg of space quanta then) we can see E=mc^2 as an equation which puts in relationship the energy of a mass with the fundamental energy of the universe (space's quanta, i.e. the real elementary scalar field) and the equation acquires a very clear sense then.
Any mass would be simply "compared" (as multiple) to the energy of a given portion of space, as for the kilogram in Sèvres.
Quantum physics indeed knows that vacuum's energy is the mother energy of particles, whose contribution is fundamental: we know that a photon is a quantum of energy. But how do you describe a photon (the energy eigenvalue of any eigenstate) without 1/2 ħω (vacuum's contribution)? Of course there's a more elementary energy field in the universe. We now call it quantum vacuum. Passing to quantum space is not a huge step, I tried to show that.
"we know that a photon is a quantum of energy"
The usual catch phrase... If a photon is a quantum (= an elementary piece of energy) it should have a definite value. Its value is according the Planck's law E=hn but n can take any value. So what does you mean, besides the usual ...
The fundamental prerequisite is that we describe the physical reality through physico-mathematical models that just represent it. The theoretical evidence is that mathematical analysis gives a continuous representation of the tridimensional geometric space. In physics instead we have to make use of measurable discrete quantities in order to formulate relations among different physical quantities. Also with regard to space we measure discrete lengths that the technological progress allows to do always smaller. On this account I wrote in preceding comment "a discrete space into the continuum", that is the basic model of space in TR. Quantization of the physical reality, or better of some aspects, derives from quantization laws that are imposed by particular physical situations, like the quantized orbital structure of electrons in atom, where the quantization is a consequence of the atom stability. Photons and energy quanta have a quantum structure because they come from the quantized reality of atoms and not of space. When Planck studied the spectrum of black body he quantized the constant h (called then Planck's constant) but it is manifest that Planck's relation is continuous with respect to the frequency that for energy quanta cannot go down under a threshold value.
If the physical reality is described through vector fields it is manifest that we can make use of the concept of flow that is related to the concept of force. It wasn't possible to Newton who didn't know the concept of field, that was introduced in physics much time after and he considered gravity like force at distance, and it wasn't used by Einstein who preferred the tensor scalar model of field rather than the physico-mathematical model of vector field.
"we measure discrete lengths" what else?
"like the quantized orbital structure of electrons in atom, where the quantization is a consequence of the atom stability.": = nonsense too, the H-atom has a discrete- (=bound, E0) spectrum, both are part of quantization of the Coulomb problem (third part: E=0)
Just, what else? you can measure only discrete quantities.
About frequency spectra, it needs to do suitable differences between continuous spectra of condensed matter and discontinuous spectra of single atoms.
Anyway I am in no mood to quibble but if possible I would want to do a relaxed discussion.
1) The theory of relativity prohibits massive body to move at the speed of light.
2) Moreover, 4-dimensional kinematics of relativity theory does not allow to describe the motion of massive body at the speed of light.
3) In contemporary physics we use the different terminology. The mass is just "rest mass". The so called "relativistic mass"? which depends on velocity does not considered as mass, it is just energy, converted to units of mass.
@ Daniele Sasso: You are not in the mood to quibble? I tell you, you just don't understand the hydrogen spectrum, and not advanced quantum mechanics in addition.
I do not think it is necessary to complicate the maths un-necessarily with 4D manifolds etc used in GTR
The equations are straight forward
Delta E = gamma. m0c^2- m0c^2
where gamma = 1/sqrt (1-v^2/c^2)
which gives a mass of infinity at v=c.
And by the way it is clear that as c is a constant then it must be the apparent mass that must increase.
Dear Anton, you write I don't understand the hydrogen spectrum, but I don't understand you, perhaps because of different languages that are translated into English. Regarding Quantum Mechanics I inform you I did exhaustive research about that very important section of physics that I formalized in several papers. Let me indicate two papers:
https://www.researchgate.net/publication/211874241_Basic_Principles_of_Deterministic_Quantum_Physics
https://www.researchgate.net/publication/211557339_Deterministic_Theory_of_the_Tunnel_Effect_in_the_Esaki_Junction
I hope to have interpreted correctly your thought.
Article Basic Principles of Deterministic Quantum Physics
Article Deterministic Theory of the Tunnel Effect in the Esaki Junction
Caro Daniele, just tell me, what is the difference in case of H-atom with respekt to the electron if E is bigger or smaller zero?
Dear Anton, in regard to questions that you raise, as per DQP and TR, I think:
1) In the event of bound electron inside of hydrogen atom in a force field with central symmetry, for E0 the motion is stable. Consequently in hydrogen stable atom E>0 must be in order to have a stable orbital motion.
2) In the event of free electron in a force field, that doesn't have central symmetry where electron moves with linear speed, electron is stable for smaller than the critical speed where E>0 and electrodynamic mass is positive. For E=0 electrodynamic mass is zero and the speed is equal to the critical speed. For E
Daniele @
Your last answer is puzzling, which may be due to different interpretations of words. I am sure you know how energy E is defined in a non-relativistic description of the hydrogen atom. How does your definition of energy relate to that use?
Not sure where this is going, isn't SR correct- surely the question is why is it correct?
Answers without referring to 4D manifolds, (ie as near as to zero gravity as you can get where GTR effects are near infinitesimal)
With the greatest of respect stop navel gazing.
Dear Kare, in the study of stability of hydrogen atom in DQP I was precise: kinetic energy was used.
But kinetic energy is always positive. The common definition is kinetic plus potential energy.
> In this situation total energy is null.
For the proton-electron system (i.e., hydrogen atom), mainstream quantum physicists would say that the total energy is negative when the electron is bound to the proton, and positive when the hydrogen atom is ionized (i.e. when the electron may move freely with respect to the proton), and that only the first case corresponds to a discrete spectrum of quantum states. With the mec2-contribution not included in the definition of E, as is common practice in non-relativistic physics.
In mainstream quantum physics , in the absence of relativistic considerations, the total energy of electron in hydrogen atom is negative and it depends on distance r of electron from proton too. It is easy to deduce in these conditions the Principle of Energy Conservation isn't respected because the total energy of system in any physical condition isn' t constant but it depends on r. In DQP instead the total energy is constant and null in any physical condition for which the PEC is always verified.
It is easy to verify then the relativistic correction in mainstream quantum physics, through the term mec2 isn't able to solve the problem. In DQP instead the relativistic correction, that consists in considering the variation of electrodynamic mass with the speed, allows to obtain the hyperfine structure of hydrogen atom and Lamb's shifts.
Daniele@ I have to trust your authority on this --- since I have no motivation to check for myself.
Dear Kare, I have appreciated much your availability to compare a controversial question with me. Thanks for your kindness and I hope in a next future you will confirm not only your consideration of results that have been obtained in my research but a convinced and motivated support. Thanks.
Ales> ..thread: "Universe is static!!! Yes or no?"
That thread is a proof that Perpetuum Mobile can exist, and can generate a lot of entropy...
Dear all
continuing the discussion in this thread, How about the emission of vacuum Cherenkov radiation, which should be prohibited by the Special theory of relativity, can someone give the reason for its emission
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