Tuesday, April 02, 2019

Dear Dr B: Does the LHC collide protons at twice the speed of light?

I recently got a brilliant question after a public lecture: “If the LHC accelerates protons to almost the speed of light and then collides them head-on, do they collide at twice the speed of light?”

The short answer is “No.” But it’s a lovely question and the explanation contains a big chunk of 20th century physics.

First, let me clarify that it does not make sense to speak of a collision’s velocity. One can speak about its center-of-mass energy, but one cannot meaningfully assign a velocity to a collision itself. What makes sense, instead, is to speak about relative velocities. If you were one of the protons and the other proton comes directly at you, does it come at you with twice the speed of light?

It does not, of course. You already knew this, because Einstein taught us nothing travels faster than the speed of light. But for this to work, it is necessary that velocities do not add the way we are used to. Indeed, according to Einstein, for velocities, 1 plus 1 is not equal to 2. Instead, 1+1 is equal to 1.

I know that sounds crazy, but it’s true.

To give you an idea how this comes about, let us forget for a moment that we have three dimensions of space and that protons at the LHC actually go in a circle. It is easier to look at the case where the protons move in straight lines, so, basically only in one dimension of space. It is then no longer necessary to worry about the direction of velocities and we can just speak about their absolute value.

Let us also divide all velocities by the speed of light so that we do not have to bother with units.

Now, if you have objects that move almost at the speed of light, you have to use Special Relativity to describe what they do. In particular you want to know, if you see two objects approaching each other at velocity u and v, then what is the velocity of one object if you were flying along with the other? For this, in special relativity, you have to add u and v by the following equation:


You see right away that the result of this addition law is always smaller than 1 if both velocities were smaller than 1. And if u equals 1 – that is, one object moves with the speed of light – then the outcome is also 1. This means that all observers agree on the speed at which light moves.

If you check what happens with the protons at the LHC, you will see that adding twice 99% of the speed of light brings you to something like 99,9999% of the speed of light, but never to 100%, and certainly not to 200%.

I will admit the first time I saw this equation it just seemed entirely arbitrary to me. I was in middle school, then, and really didn’t know much about Special Relativity. I just thought, well, why? Why this? Why not some other weird addition law?

But once you understand the mathematics, it becomes clear there is nothing arbitrary about this equation. What happens is roughly the following.

Special Relativity is based on the symmetry of space-time. This does not mean that time is like space – arguably, it is not – but that the two belong together and cannot be treated separately. Importantly, the combination of space and time has to work the same way for all observers, regardless of how fast they move. This observer-independence is the key principle of Einstein’s theory of Special Relativity.

If you formulate observer-independence mathematically, it turns out there is only one way that a moving clock can tick, and only one way that a moving object can appear – it all follows from the symmetry requirement. The way that moving objects shrink and their time slows down is famously described by time-dilation and length-contraction. But once you have this, you can also derive that there is only one way to add velocities and still be consistent with observer-independence of the space-time symmetry. This is what the above equation expresses.

Let me also mention that the commonly made reference to the speed of light in Special Relativity is somewhat misleading. We do this mostly for historical reasons.

In Special Relativity we have a limiting velocity which cannot be reached by massive particles, no matter how much energy we use to accelerate them. Particles without masses, on the other hand, always move at that limiting velocity. Therefore, if light is made of massless particles, then the speed of light is identical to the limiting velocity. And for all we currently know, light is indeed made of massless particles, the so-called photons.

However, should it turn out one day that photons really have a tiny mass that we just haven’t been able to measure so far, then the limiting velocity would still exist. It would just no longer be equal to the speed of light.

So, in summary: Sometimes 1 and 1 is indeed 1.

58 comments:

  1. Not for posting. Perhaps a post by you.

    But, you can discombobulate people even more by noting that sometimes, 2 * 2 = 0. I have done this even to high end (NAS member) theoretical chemists! Of course, the ones have to be the values of variables, say the numerical value of the "electron field" at a given spot. No, you say to them, I do NOT mean the "electric" field of electromagnetism, I mean the quantum field of the electrons themselves. You then explain anticommuting variables and Grassmann numbers, and how that explains the Uncertainty Principle. There are even physicists who never heard of this. I would expect chemists to never have heard of them, but not modern physicists!

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  3. Depends on the context. The relative velocity that is relevant for defining cross sections in terms of particle fluxes is the Moller velocity. In the limit you mention the Moller velocity is actually 2 times the speed of light.

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  4. Sabine Said… “This does not mean that time is like space – arguably, it is not…”

    Can you give me some arguments as to why time is not like space? When I visualize your explanation and other relativity examples the only argument I can come up with is, intuitively we think that way. Both are always physically relative to each other (space is physically relative to time and vice a versa). I can express a light year in distance or time; either way there is a single physical meaning for the two ways to express it. Physically I only see a single phenomenon where both expressions are concerned?

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    1. Louis,

      There is only one time dimension but three dimensions of space.

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    2. As I understand it the directions of space are the same as the directions of time.

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    3. Louis and Marten,

      There is a wonderful old book by Hermann Bondi, Relativity and Common Sense, that explains what is happening with only some minimal high-school algebra and a lot of physical examples.

      I taught myself Special Relativity (and basic algebra) from this book in seventh grade.

      By the way, another respect in which time is different than space is that there is an analogy to Pythagoras' Theorem in relativity, but the time-squared term enters with a minus sign relative to the space terms.

      There is lots of other stuff going on, related to hyperbolic trig functions, hyperbolic geometry, etc.

      Special Relativity is fun.

      Dave

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    4. What about Euclidean space-time?

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    5. Here's a (reasonably accurate, albeit in many ways incomplete) picture.

      Imagine a double-cone (the "light cone" as we call it). The stuff inside is "timelike," the stuff outside is "spacelike."

      Note that I can't move the inside stuff outside, or vice versa, without pushing something "through" the light cone. In that sense, being spacelike and timelike are distinct.

      Furthermore, they're different: I have two "spacelike" directions from the cone, and one "timelike" direction (in some sense of counting them that is made more precise with the actual math). So, spacelike and timelike are not only distinct, but *different* in that sense.

      Nevertheless, the spacelike and timelike "parts" are related, living in the same "space" and having that cone in-between. This is the inseparability of the two as "spacetime," despite them being different things.

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    6. marten,

      Well, spacetime just is not Euclidean: the term is "pseudo-Euclidean" ("pseudo" not meaning fake but rather similar to) or, more properly "Minkowskian."

      One important consequence of this is that if you try to "rotate" time into space, both the time axis and the space axis move towards the "light cone" that APDunbrack described. If time and space were simply parts of a true Euclidean space, of course this could not happen.

      Let me emphasize that this is not some crazy speculation that physicists made just for the fun of it. This is a necessary consequence of some very simple facts about the physical world (basically, the fact that the speed of light is the same, regardless of the speed of the source or of the observer). There is no way to show you why this is true in a brief comment here: you just have to go through the physical examples in, say, Bondi's book. Of course, Wikipedia also has articles, but I think you will find Bondi clearer.

      Dave

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    7. Dave,

      For various reasons I have strong doubts about the standard theories in physics and cosmology. In contrast I find it plausible the way Hawking in his Brief History of Time, Chapter 8, describes Euclidean space-time and its consequences.

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    8. marten,

      We're talking apples and oranges. Hawking's Euclidean spacetime was a very speculative idea, without any real evidence and not accepted by most physicists, as to how the Big Bang could have started -- how to get something out of nothing.

      I assure you that Hawking did not believe that spacetime at present is Euclidean! If you think that was what he was saying in A Brief History of Time, you misunderstood him. I have actually met Hawking and read a fair amount of his writings; I studied under his friend and colleague Kip Thorne.

      Physics is not a spectator sport: if you actually want to understand this stuff, you need to roll up your sleeves and dive in to something like the Bondi book and understand the algebra and work through concrete examples.

      When I started learning Special Relativity, I, like you, wanted time to be another Euclidean dimension. But, one of the main points of Sabine's book is that what we want Nature to be does not really matter.

      Nature is what it is. It is our job to make our thinking conform to the reality of the natural world -- even if that reality is not what we find beautiful or simple.

      All the best,

      Dave

      All the best,

      Dave

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    9. Dave,

      By the way: the first Physics book that I ever bought, still in my bookshelf, I have studied it numerous times, is Die Evolution der Physik by Albert Einstein and Leopold Infeld (rowohlts deutsche enzyklopädie).

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  5. doubled word 'then'.
    "...one object moves with the speed of light – then then the outcome is also 1."

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  6. It is worth noting where this comes from for those not mentally marinated in physics. The transformation of dx and dt with dx/dt = u to another frame with velocity v and γ = 1/sqrt{1 - (v/c)^2} gives this result. We have dx = γ(dx - vdt) and dt = γ(dt - vdx), with c → 1. There is an implicit sign change for particles moving towards each other with a u·v = -|u||v| and dx – vdt → -|dx + vdt|, which then gives

    u' = dx'/dt' = (dx + vdt)/(dt + vdx) = (u + v)/(1 + uv)

    for u and v the same magnitude and v → 1 this is u' ≈ 1 or close to the speed of light.

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    1. “… for those not mentally marinated in physics.” ;-) – and maybe algebra … here some steps added:
      u' = dx'/dt' = (dx + vdt)/(dt + vdx) = dx/(dt + vdx) + vdt/(dt + vdx) = dx/dt /(dt/dt + vdx/dt) + vdt/dt /(dt/dt + vdx/dt) = u/(1 + vu) + v/(1 + vu) = (u + v)/(1 + uv)

      We also can make the Galilean way of adding velocities u + v a multiplication by putting u and v in 2*2-matrices with diagonal elements 1: (1,0,u,1)*(1,0,v,1) = (1,0,u+v,1)
      Realizing that u/c²≈0 for u≪c we can write u again as 2*2-matrix. “Adding” u + v by multiplying (1,u/c²,u,1)*(1,v/c²,u,1) we see (u + v)/(1 + uv/c²) emerging.

      Galileo treated space and time not symmetrically, because there was no “Maxwellian” speed limit c yet.
      Lorentz transformation is a central extension, it contracts to Galileo when c→∞.
      But still the main difference between time and space, besides the dimensions is that we cannot go back in time. Sure, SR, GR and QM each separately are time reversible. Only temperature and entropy are fighting against it.

      Sabine’s “This observer-independence is the key principle of Einstein’s theory of Special Relativity.” stresses observer-independence in Galilean relativity. The apparent conflict between observer-independence and c=const was resolved by taking both for real. The solution of SR was not to decide exclusively for one or the other.

      Maybe exclusively unitary evolution in QM is broken. I guess the measurement problem is telling us all the time, that QM is only unitary between observer-independent triggered reductions, measurements. With each observer-independent measurement entropy is added, breaking the symmetry of time and the block universe.

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    2. This is probably the best way to think about it. You can repeat this approach for the conformal group, which introduces a fixed 4-vector A_n into the transformation formulas. You can then ask what is the transformation for velocity when dealing with very remote objects. It turns out that when A_n is timelike, a distant object at rest has an apparent radial speed proportional to its distance :) Things that make you go "hmm"!

      -drl

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    3. Spacetime as a role with unitarity in that it converts it into hyperbolic transformations. The elementary case is with the accelerated frame. An accelerated observer, g = acceleration, is on a hyperbolic path that asymptotes to a split horizon. The two horizons occur at some arbitrarily chosen origin. A quantum flutuation as a loop at this origin with a radius r has null geodesics connecting it to the accelerated frame. Assume this accelerated observer approaches within r = c^2/g of the origin. Then the observer has causal contact with the loop throughout this Rindler wedge. The loop parameterized by a time or length d = 2πr = 2πct and in Euclidean time, since this is an off shell state and an instanton, the unitary operator e^{-iHt/ħ} → e^{-2πħωrħ}. Here the Hamiltonian is assumed to give energy ħω. Substitute in r = c^2/a we have a Boltzmann term e^{-2πħωc/g}. An identification of this with e^{-E/kT} leads easily to the temperature

      T = ħg/2πkc.

      So temperature is the same as acceleration! This is a quick an dirty derivation of Unruh radiation, which I will admit glosses over some points. Some work and the identification of the acceleration with a black hole gives Bekenstein-Hawking temperature for a black hole.

      We commonly think that because of this everything is lost. Gravitation makes a hopeless muddle of quantum mechanics because of these. However, really what this does to operators a and a^† is to transform them into

      A = a cosh(gs) + a^† sinh(gs), A^† = a^† cosh(gs) + a sinh(gs).

      Now the commutator [A, A^†] can be easily seen to be equal to [a, a^†] = 1. The phase space volume of the operators is conserved. There is no information loss. Now if we has incomplete knowledge, such as where the origin s = 0 is, then we would tend to coarse grain with cosh(gs) ~ e^{gs} and sinh(gs) ~ e^{gs} and we would have [A, A^†] ~ e^{2gs}. The phase space volume is growing which indicates there is noise entering the system that expands the phase space volume by stochastic processes. This then gives the appearance of there being the increase in temperature with time.

      The difference between unitary evolution and this hyperbolic evolution is that time is in a sense imaginary valued. This occurs in general for instantons and tunneling states. There was recently announced the measurement by a group in Australia of the time for tunneling as 1.8 attoseconds or less. The phase (ħ/√2m)√{E - V} t is imaginary valued for V > E, and we can just as well think that t → it. Hawking did a lot of work with gravitational instantons in imaginary time. I have not seen it but this Z_2 group for time might be too restrictive and we might as well then think of there being a U(1) group for a complete set of complex valued times. This might connect with BMS transformations and gravitational memory,

      The funny thing is that entropic time violates T and P. The violation of T symmetry is obvious. A violation of parity is more subtle, but if I send in a beam of polarized radiation into a black hole that information is not in the coarse grained “hair” of a black hole and is then lost. This means ultimately that CPT discrete symmetry appears violated. We are then at a loss as to whether quantum gravitation in demolishing information violates CPT. However, my argument with the operators gives a glimmer of light saying that it does not. I would then say that CPT violation, and ultimately the occurrence of entropic time, is due to our description of nature. There are apparent causality violations in the EPR type of experiments, but on deeper study we find there are no signaling of causal events. I would argue in much the same way that entropic time is a very similar sort of illusion.

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    4. drl and Lawrence,

      @drl
      I also was awestruck when I first heard that de Sitter spacetime is a coset manifold SO(4,1)/SO(3,1) – I thought the creator at least must have studied groups and loves complex numbers. OTOH our world is not this perfect beautiful symmetric place as mentioned here.

      @Lawrence
      Thanks for your response and I need some more time to answer.

      Since both of you mentioned Terrell rotation … when I first learned about this I thought – that´s handy, then a black hole horizon is just rotated and its Bekenstein-Hawking-entropy is invariant. And now it might be good for Verlinde’s area versus volume entropy threshold.

      - Typo: (1,v/c²,u,1) should be (1,v/c²,v,1).
      - And just to mention multiplying with 1=(1/dt)/(1/dt) would have been enough – sorry, my bad – lost in algebra.

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  7. If there would be a length contraction by movement, the sun would have to be an ellipsoid for an moved observer.

    But the sun is no distinct ellipsoid. Impartial! Objective! The shape of the sun is nearly sphercial. And this is the fact, because the known astro-physics is valid and by that, the sun have to be spheric.

    So there is no length contraction anywhere.

    The length contraction is a deception for an observer - comparable with the deception that something in the distance seems to be smaller than if it is close by.

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    1. I do not have a lot of time to delve into this. I do give this link

      https://www.youtube.com/watch?v=JQnHTKZBTI4

      of a video on the Terrell rotation. There are optical aspects to the appearance of lengths. Light from different parts of a body take different time to reach the observer. Without length contraction a sphere would really be length expanded and the Lorentz contraction exactly cancels that. So a moving sphere appears as a sphere, but rotated. A cube approaching you would appear rotated upwards. The optics gets a bit complicated as this video illustrates based on numerical simulation.

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    2. Lawrence Crowell 7:19 AM, April 03, 2019

      Do you agree to the following sentences:

      "An objective fact holds for any observer!"
      and
      "It is an objective fact which follows from our know physics, that the sun has a nearly spherical shape!"
      ?

      If so, what means "length contraction following from SR"?

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    3. A body moving twoards you, say a sphere or cube appears as such, but it they are not moving towards you they appear rotated. There are optical aspects to this. This really is not that objectively different than if one looks at something through some distoriting lens.

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    4. Weistdas asked Lawrence:
      'Do you agree to the following sentences:

      "An objective fact holds for any observer!"
      and
      "It is an objective fact which follows from our know physics, that the sun has a nearly spherical shape!"'

      When scientists say that the shape of the sun is a sphere, they mean in the rest frame of the sun.

      In other frames of reference, it is not a sphere.

      You can argue about the real meaning of "objective," but that does not matter: note that I did not need to use the word "objective."

      As Lawrence has mentioned, how it looks visually in a certain frame of reference is different from its actual shape.

      Reality is complicated, whether we like it or not.

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    5. PhysicistDave10:48 PM, April 05, 2019

      "When scientists say that the shape of the sun is a sphere, they mean in the rest frame of the sun."


      So, in other "frames" there has to be other physical laws? The shape of the sun is determined by our physical laws. This laws and the shape of the sun correspond mutually. This laws and an ellipsoid sun doesn't correspond mutually. In fact they contradict mutually.

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    6. Lawrence Crowell10:44 AM, April 04, 2019

      "A body moving twoards you, say a sphere or cube appears as such ..."

      You are not familiar with the concept of length contraction in special relativity?

      That's here the point.

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    7. Of course I know about Lorentz contraction. I first learned about it as a sophomore in high school. The optics is such that objects do not appear contracted. In fact in Galilean relativity of Newtonian mechanics objects would appear elongated based on ray tracing optics. The Lorentz contraction exactly cancels that out.

      Contraction only appears with gravitation with the Lorentz gamma factor

      Γ = 1/√(1 - v^2/c^2 - 2GM/rc^2)

      where contraction occurs up to zero limit on black hole horizons.

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    8. Lawrence Crowell8:37 PM, April 12, 2019

      Who cares about optics by that concern? You have never heard about "length contraction" by special relativity?

      The claim is, that an observer measures a moving object in the moving direction shorter. And the claim is, that this contraction would be real. Fast space ships would have a shorter way to a distant target than slower space ships.

      In special relativity the length contraction corresponds with the time dilation. They are two sides of one coin. If length contraction is unreal, time dilation is unreal either.

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    9. In relativity coordinates are very secondary. It is often said that we do physics in a coordinate independent framework. Coordinates are something the analyst imposes on a problem, or a reference frame an observer chooses. Coordinate transformations in spacetime are more than three dimensional rotations, but involve nonEuclidean rotations between space and time. Coordinates are then not an absolute aspect of spacetime geometry, but rather projective rays for the speed of light are.

      I suggest that you study this, for it is apparent you are pretty confused and twisted around on your thinking about this. Things like coordinate distances and time are transformable and what is invariant is the speed of light or null directions. I can't in this little forum provide in depth education on this.

      I generally avoid arguing with creationsists, because such people have their opinion fixed and the real science is denied. I have seen similar occurrences with physics, and you appear to be such a case. I have run into quantum deniers and sometimes relativity deniers. It appears here there is not much I can do to persuade you in ways contrary to you thinking.

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    10. weristdas,
      this series here will help you to build a better intuition what SR is about.

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    11. Lawrence Crowell6:31 AM, April 14, 2019

      Reference frames or coordinates, reference systems, Bezugssysteme, inertial systems, …, what you like. All the same in that concern.

      So, what had you say other than you want to bring me in neighborhood to creationists? Shame on you by "arguing" like that.

      The muon has the same way towards the earth as the earth has the same way towards the muon. Whatever reference system you choose. Only the direction is reversed from one to the other.

      The muon has the same speed towards the earth as the earth has the same speed towards the muon. Only the direction is reversed from one to the other.

      And now bring arguments why the earth should have to move 14.000 meters to the muon, but the muon should have to move only 600 meters to the earth. Without insults! Better be silence. And learn something about relativity of movement.

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  8. Has the formula ever been experimentally tested for mid-range velocities (for example u = v = 0.5 c or 0.6 c)?

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    1. FLorian: In the history of accelerators, >> https://en.wikipedia.org/wiki/Particle_accelerator

      it looks like early cyclotrons were working in the 0.1c up to .8c for the next generation. It says 0.1c is when relativistic effects start to become a problem and required new engineering, so I think your answer is yes. If they had discovered anything amiss with relativity in that range, we'd know about it.

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  9. In moving particle, the Lorentz transformation approach used and not the gallolean transformation approach. So not fully additive the speed of particle after hitting and back

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  10. Moving spherical objects always appear spherical, regardless of their state of motion. The Lorentz contraction is an effect in 3D space but not in spacetime - it does not refer to a spacetime-invariant configuration. However the pencil of light rays from the Sun that defines its shape, *does* refer to a spacetime-invariant configuration, and that shape is not determined by the Lorentz contraction alone. This is related to the "perfect eclipse" problem. Let the the perfectly spherical Moon exactly eclipse the perfectly spherical Sun when the Moon is standing still. Now give the Moon a sideways shove. Does the eclipse still happen? (Answer - yes.) ALmost all the confusion in relativity arises from lack of proper identification of spacetime invariant configurations.

    -drl

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  11. Sabine wrote:
    " ... Special Relativity we have a limiting velocity which cannot be reached by massive particles, no matter how much energy we use to accelerate them. ... should it turn out one day that photons really have a tiny mass that we just haven’t been able to measure so far, then the limiting velocity would still exist. It would just no longer be equal to the speed of light."

    I thought limiting velocity = c, and independent of observer's frame, was motivated by the Michelson-Morely experiment, no?
    And since no one has measured anything having speed >c, it was assumed (or an axiom?) that photon speed in a vacuum was the "limiting speed"?

    So when Sabine writes "limiting velocity would still exist. It would just no longer be equal to the speed of light" , why does a limiting velocity exist, even for a massless particle?

    Is it an axiom, or does Special Relativity somehow mandate & require it?

    --TomH

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  12. Let me say a few words as this is a pet topic of mine.
    It is an empirical fact that there is a speed limit in nature. This fact is not acknowledged in classical (Newtonian) physics: accepting it would imply that velocities could not be added as lengths. There is a remarkable paper from 1972 (B. V. Landau and S. Sampanthar, A New Derivation of the Lorentz Transformation, Am. J. of Phys. 40, 599, (1972)) that exhibits this approach in just three pages. And sure, light has no role in this - it is just a short name for "fastest signal". In Einstein's time there was a widespread conviction that mass is intimately connected to electromagnetism and much of this lingers on. It is difficult to convince the public that there is nothing essential in light itself, it just happens to be one example among the things ("luxons") that reach the maximum speed.

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  13. I don't talk about how something appears. The SR says, that a moving object contracts in the moving direction for the observer. If the sun moves relative to an observer (sun and observer are in relativ movement to each other) the diameter of the sun in moving direction have to be contracted for the observer. So the shape of the sun is an ellipsoid for the observer. But that infringes the valid physics which has also hold for the moving observer. The sun is spherical by the physical laws and their mass, the gravitation, the stage of development, the radiation pressure, ...

    So the length contraction has to be an pure illusion.

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  14. If the sun … and observer are in relative movement to each other, the diameter of the sun in moving direction have to be contracted for the observer. So the shape of the sun is an ellipsoid for the observer.

    Stated more correctly, the sun’s shape is a contracted ellipsoid in terms of any system of inertial coordinates in which the Sun is in motion. (For simplicity we’re treating the Sun and it’s weak gravitational field as an isolated entity in a flat spacetime background, so that we can talk about its description in terms of different inertial coordinate systems, but the results apply generally.)

    But that infringes the valid physics which has also hold for the moving observer. The sun is spherical by the physical laws and their mass, the gravitation, the stage of development, the radiation pressure, ...

    No, in terms of a system of inertial coordinates in which the Sun is moving, the laws of physics all yield a contracted ellipsoidal shape. This was actually known prior to special relativity. For example, it was known in the late 1800’s that Maxwell’s equations imply that, in terms of a single system of coordinates, the spatially spherical shell of equal potential around a charge contracts into an ellipsoidal shape when the charge is set in motion, by the factor sqrt(1 – v^2/c^2). Poincare explained that this necessarily applies to any physical potential that propagates at the speed of light, and this includes the effects of both electromagnetism and gravitation, as well as the strong and weak nuclear forces. (The fact that gravity has ten potentials in general relativity, affecting the local metric, doesn’t alter this conclusion.)

    So the length contraction has to be an pure illusion.

    Not at all. As noted above, all the known laws of physics are locally Lorentz invariant, which signifies that the equations take the same form in terms of any local system of inertial coordinates, which are related by Lorentz transformations. Hence a shape that is formally spherical in terms of one system of coordinates is formally a contracted ellipsoid in terms of another, and the equilibrium shape of any defined object will conform with this when its state of motion is changed. Again, for gravitational effects this is easiest too see in weak field situations (like the Sun) that can be described as an isolated object in a flat background, but it applies in general. You can read about this in any good book on relativity.

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  15. I would suggest that the amount of imperfections created by packing a sphere with spheres is equal to the surface area of the outer part of the larger sphere. Imperfections are the only way to store information and that is why the amount of information is equal to the outer surface.

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  16. First, I talk about an ideal object what the sun only nearly should be. The sun is just an example. See the sun here as an ideal object.

    Second, the shape of an ideal object like the sun is determined by the known physics.

    Third, the diameter of such an object is determined by the known physics.

    Fourth, I don’t talk about what somebody might see or observe, I talk about objective facts.

    Fifth, objective facts are objective facts because they hold for any observer - if they observe them - or if they observe them not!

    Sixth, the spherical shape of an ideal gas accumulation (similar as the sun) in an otherwise empty space and with enough time for development is a fact.

    Seventh, do a theoretical non-interacting particle (perhaps a neutrino) which moves with relativistic speed to the sun through the center of the sun has a way of the known diameter of ~1.4 million kilometers within the sun? If not (because of the SR length contraction), how can the sun have a spherical shape and an ellipsoid shape at the same time which is not compatible with objectivity in physics?

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  17. When I visualize this symmetry, I think of the signature mentioned by PhysicistDave. A spatial line element from continuum mechanics is often portrayed using the diagonal of a cube. Three edges of the cube are labeled with the spatial directional differential elements. The diagonal is given its corresponding direction.

    If one were describing a moving particle, one would associate the origin for the time parameter at the same vertex. But, if one is thinking of time as limiting the spatial volume, its fixed origin must lie at the terminal end of the line element.

    This is actually similar to how I first thought about the orthogonality of time as a dimension. As one increases the number of spatial elements, the angles between the line element and the coordinate axes approach right angles. In the limit, what had been the line element is orthogonal to all spatial dimensions.

    It is somewhat simplistic -- and entirely without a physical ground -- but I tend to seek visualizations when trying to reconcile different parts of mathematics.

    Great topic, great comments. Thanks Dr. Hossenfelder.

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  18. I assume you did not publish my last reply because you thought it violated your comment rules. I referenced the spacetime comments to physically observable change and that was factual, I also accurately referenced documentation from the US naval observatory and NIST (available on request) regarding the operation of atomic clocks (I read your blog post about them a while ago and you missed mentioning the quartz oscillator in a feedback loop with the microwave emitter). It is extremely difficult to observe nature without bias or preconception, that’s the only thing I try to do (see, to what extent I can, what nature does, limit, check, and recheck my bias when doing it).

    ReplyDelete
  19. The people who claim to understand special relativity say that a muon, which come into existence in the atmosphere at a height of approximately 14.000 meters, has only to fly 600 meters to hit the ground.

    That's similar as to say, two vehicles are at crash course, the first one is 14.000 meter away from the other, the other is 600 meters away from the first one.

    Relativity means that movement is relative. There is no difference between object A and object B which are moving relative to each other. So, no one can explain the difference between the two objects, why the one is 600 meters away, the other is 14.000 meters away from the other.

    Special relativity is inconsistent within itself.

    (I know that they say, the different distances are measured in different coordinate systems. But what changes that? In both coordinate systems the objects are in different distances to each other. That's impossible.)

    ReplyDelete
  20. Relativity of movement means, that we can see the muon moves to the earth with nearly light speed, as we can see the earth moves to the muon with nearly light speed.
    So, why should the earth has to travel 14.000 meters to the muon, but the muon only has to travel 600 meters to the earth?
    There is no plausible cause for that asymmetry.
    Length contraction by special relativity is unfounded and inconsistent.

    ReplyDelete
  21. The best text on special relativity "for beginners" that I know is "It's about time" by N. David Mermin.
    Check it out! :)

    ReplyDelete
    Replies
    1. I would suggest to use texts on "self-thinking" before starting to read about relativity.

      Delete
  22. I think a vasistas can best be used in combination with a rétroviseur :-)

    ReplyDelete
  23. I have to say that, in my eyes, anybody who sticks to the idea that two objects which moves to each other should have permanently or even only sometimes have different distances to each other is completely confused.

    ReplyDelete
  24. I have discussed this issue with different specialists on relativity, and nobody was able to proof this argumentation wrong until now:

    Relativity of movement means, that the muon moves the same path towards the earth as the earth moves the same path towards the muon. Both passes this path with the same speed. Only the direction is reversed.

    Relativity theory says nothing concerning the direction of a movement.

    So, why the length of the path should be other in the one direction than in the other direction? Why should the muon have to travel 600 meters while the earth should travel 14.000 meters until contacting each other?

    ReplyDelete
  25. Why is the length of the path different in one direction than in the other? Why should the muon have to travel 600 meters while the earth should travel 14000 meters until contacting each other?

    You overlooked the relativity of simultaneity, and the difference between objects and events. Let S be inertial coordinates in which a particle P on the earth’s surface is at rest, and let S’ be a system in which the muon is at rest. The muon, directly approach P at high speed, is created at event E1, which is simultaneous with event E2 of P in terms of S, and with event E3 of P in terms of S’. You specified that the absolute interval between E1 and E2 is 14000 meters, and the absolute interval between E1 and E3 is 600 meters, so E3 is 46.62 microseconds later than E2. There's nothing paradoxical about this. The two absolute space-like intervals (14000 and 600) are between two different pairs of events.

    Needless to say, for each particle, when it is a given proper time from collision, in terms of it's own rest frame coordinates the spatial distance to the other particle is the same.

    ReplyDelete
    Replies
    1. DanCo1:17 PM, April 15, 2019
      "The two absolute space-like intervals (14000 and 600) are between two different pairs of events."

      No. The muon is allegedly never ever more than 600 meters away from the earth. In none frame, none coordinate system, none reference system, none inertial coordinates, ...

      It is the usual way out of relativity theorists to say there would be a relativity of simultaneity.

      But what should that change?

      Do you disagree that the muon must move the same path towards the earth as the earth have to move the same path to the muon? (You should understand the change in the reference system within the sentence). That both have the same speed relative to each other? That only the direction is different?

      So, what have time, events to do with that?

      Delete
    2. DanCo1:17 PM, April 15, 2019

      In physics a process like these should can be considered either forward same as backward.

      So, we have a muon which starts from the earth and moves to space, as we can see the earth moving away from the muon (in system of rest of the earth and in system of rest of the muon respectively).

      The first event, the disconnection of muon and earth should be at same time, should be the same event.

      At what time begins the events for the earth and for the muon start to fall apart (in system of rest of the earth and in system of rest of the muon respectively)? And why? Both move with same speed away from each other (in system of rest of the earth and in system of rest of the muon respectively)!

      Delete
    3. "The muon is allegedly never ever more than 600 meters away from the earth. In none frame, none coordinate system, none reference system, none inertial coordinates, ..."

      I haven't followed your debate, but this statement is obviously wrong. I want to kindly recommend you continue your muon discussion elsewhere, thanks.

      Delete
    4. Sabine Hossenfelder6:47 AM, April 16, 2019

      You are right. But this was a careless mistake by me and doesn’t hurt in anyway my argumentation.

      The muon is in the muon system of rest never ever farer away from the earth than 600 meters should it mean.

      Delete

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