Questioning Relativity 16: Definition vs Axiom

· theory of relativity
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How can we know if a theory is a physical theory about some real physics or a mathematical theory which does not say anything about physical reality?

Easy enough: Look at the fundamental postulates of the theory and check if they connect to real physics or not. If there is no physics there, then there is no physics anywhere in the theory.

A postulate can take one of the following two forms:

  1. definition
  2. axiom

1. A definition is empty of content and only prescribes how to use certain words. A definition is true by its construction, as long as it is not contradictory. Example: There are 100 centimeters on a meter.

2. An axiom makes a statement about the components of the theory, which is not empty of content. Example from Euclidean geometry: Through two distinct points there is a unique straight line. If point and straight line are given a physical meaning, e.g. as single dots and collection of dots drawn by a ruler on a blackboard, then this axiom makes a statement about physical reality: Given two distinct dots it is possible to draw a unique line through the points by the ruler.

This is the distinction made in logic between analytic statements (true by definition or tautologies) and synthetic statements about reality which may be true or false depending on reality.

Let us subject Newtonian mechanics and Einstein’s theories of relativity to this test:

Newtonian Mechanics

The basic postulate is Newton’s Law

  • M\frac{dU}{dt} = F,

where M is the mass of a body moving with velocity U and acceleration dU/dt subject to a gravitational force F. This is an axiom with physical content which connects two different physical aspects: motion and gravitational force.

The axiom states that acceleration is proportional to gravitational force. This is a statement about physics which may be true or not true. It is not a definition which is true by its construction.

Newtonian mechanics is a physical theory which makes definite predictions about physical reality. Galileo prepared the theory by experiments.

Special Relativity

The basic postulate of special relativity is

  • The speed of light is the same for all observers.

Today this is a definition since the length unit is defined as a fraction of lightsecond according to the 1983 SI standard. The speed of light is today defined to be equal to 1 lightsecond per second, the same for all observers.

General Relativity

Basic postulates of general relativity are

  • Principle of Relativity: Physical laws are the same in all reference systems.
  • Principle of Equivalence: Inertial mass is equal to heavy mass.

The Principle of Relativity is a definition or truism only stating what is self-evident, namely that the expression of a physical law in different coordinate systems must connect according mathematical laws of coordinate transformation (general covariance).

The Principle of Equivalence is a definition since it defines inertial mass to be equal to gravitational mass.

The physics of general relativity enters through the right-hand side of Einstein’s equations which acts as a stress-energy source to the differential equation for the space-time geometry tensor.

Result of Test

  • Newtonian mechanics is a physical theory.
  • Special relativity is a non-physical theory based on a definition.
  • General relativity is based on two definitions plus an axiom connecting stress-energy to space-time curvature similar to Newton’s Law.

121 Comments

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  1. Mike

    Are you saying that special relativity stopped beeing a physical theory in 1983? 🙂

    Theoretical physicist are indeed aware of the distinction between an axiom and a definition.

    Let me quote from one of the standard modern texts in special relativity, Rindlers Introduction to special relativity.

    “Finally in spite of its historical and practical importance, we must de-emphasize the logical role of the law of light propagation as a pillar of special relativity. As we shall see
    in section 7(x), a second axiom is needed only to determine the value of an invariant velocity c that occurs naturally in the theory. But this could come any number of branches of physics- we need only think of the energy formula E=mc^2, or de Broigle’s velocity relation uv=c^2. Special relativity would exist even if light and electromagnetism were somehow eliminated from nature. It is primarly a new theory of space and time, and only secondarily a theory of the physics in that new space and time, with no preferred relation to any one branch.”

    I guess that this quote shows that it is your assumption about theoretical physics that is empty.

    The law of light propagation is the result of the axiom that you stated under special relativity together with the other basic axiom which the theory basically shares with Newtonian mechanics. It’s also a bit dishounest not to include the relativistic momentum law.

    (You should add these axioms under the special relativity section here)

  2. claesjohnson

    It was never a physical theory, and even less so after 1983. Einsteins two postulates for special relativity are (i) physical laws are required to take the same form in all inertial systems, (i) the speed of light is required to be constant to all observers. Both (i) and (ii) are empty of physical content since they are just requirements imposed on physics, which cannot be false.

    To require reality to behave in a certain way is not physics. Physics is to observe what actually happens as a passive observer, not to impose predetermined outcomes as an active participant.

  3. Mike

    Since it seems that you didn’t read and poundered my previous comment let me clarify with another quote from mentioned Rindler. Rindler is a standard text in the modern curriculum of theoretical physics and is probably quite representative of the philosophy used in theoretical physics.

    p. 69 say (second edition)

    “Our studies so far have essentially been elaborations of Einstein’s two basic axioms, without the addition of further hypotheses. Thus we have uncovered the structure of spacetime, and some kinematic properties of light propagation, implicit in those axioms. But now we come to the next point in theprogramme of special relativity, namely the scrutiny of the existing laws of physics and the modification of those that are found not to be Lorentz-invariant. At that stage further hypotheses are needed. For there is no logical or empirical way to prove a basic law of physics. It is a mathematical model-a human invention-that must be consistent with our limited experience, but it must also allow us to make new predictions that could, at least in principle, be falsified by further experiments. Such predictions and the attempts to falsify them (usually described as attempts to verify them) are in themselves a main stimulus to the progress of physics. Laws that cannot be falsified are tautologies. Yet Nature is strangely simple. Within a suitable mathematical framework, some of the simplest imaginable laws are the ones that Nature seems to follow, at least to the accuracy that we are able to test.”

    I think the quote stands for itsef, but let me clarify, it is to my personal experience a quite representative view that I myself experience to have encountered when studying physics and interacted with working theoretical physicists.

  4. claesjohnson

    Rindler illustrates my point that physicists are confused about the relation between math and physics/reality. Of course it should be possible to test the validity of a physical law, if it is not simply a definition or mathematical tautology.

  5. Mike

    What physicists are you talking about?

    As I wrote, the view that Rindler describes is standard.

    You should read up on relativistic kinetics and see what theory that survives when doing conservation experiments, Newtonian or special relativity.

  6. Mike

    And when your at it, read up on special relativistic test theories to, you will end up there sooner or later anyway if your interested of the validity tests of special relativity.

  7. claesjohnson

    Many physicists seem to muddle math and physics following Einstein. To make real experiments with human observers in different inertial frames traveling with a speed comparable to the speed of light seems utterly impossible in practice. Only “thought experiments” are possible and these are not real experiments.

  8. Michael

    It seems to me that the results of the experimental measurement of the muon stopping rate at two different altitudes prove that the time dilation effect of special relativity is a real fact.
    Then I ask me: if, as you say, the relativity is unphysical, what do we really measure making that experiment?

  9. claesjohnson

    The decay of muons in the atmosphere is probably a complex story, and the explanation that they have clocks which seem to slow down when viewed by human observers according to the time dilation of SR, seems to me utterly farfetched scientifically. If time dilation according to SR is a real phenomen there should be massive experimental support, not just a few observations which cannot be immediately explained.

  10. Mike

    There seems to be some confusion about decaying muons (or other decaying particles I assume) and time measurement. Let me see if there is a way to clarify this from a special relativistic point of view.

    Is there a way to argue that the time of a physical process, like the mean lifetime of muons, is connected with the time measured by a clock, assuming special relativity?

    Yes there is. There is an argument that I think originally was given by Feynman.

    First let us notice that this is an argument that assumes that special relativity is true.

    So we have the principle of relativity, originally several hundred years old. Let us formulate it in a useful form:

    (a1) Situated in a space ship, with no windows, moving with constant speed relative to another spaceship that we say is at rest, there is no possible way of conducting a physical experiment that let you determine your velocity relative to the non moving spaceship.

    We also have the axiom about light in inertial frames

    (a2) There exist an inertial frame in which light signals in vacuum always travel rectilinear at constant speed c, in all directions, independent of the motion of the source.

    Combining these two we get the law of light propagation

    (l1) Light signals in vacuum are propagated rectilinearly, with the same speed, at all times, in all directions in all inertial frames.

    Let us then construct a clever (but maybe unpractical clock) that can be used to examine time. The ingenious idea is to base the clock on light signals.

    Assume that we have two similar rods of equal length L. Attached in one end is a mechanism that emits a light pulse (today we have cool lasers for this purpose) and a photocell that detects light, triggers a counter and finally stimulating a new pulse. In the other end is a mirror reflecting the light from the light emitter to the photocell. Assume that the two light clocks are well synchronized.

    For a light clock in a rest frame, light travels the distance 2L, straight up straight down, during the time t = 2L/c and this is taken as a clock cycle. For a rod moving with constant velocity v in this rest frame light travels, velocity perpendicular to the rod (i.e. there is no length contraction of the rod), according to (l1) in a triangular shape, not straight up but along a tilted linear path, bouncing and following a tilted linear path back to the photocell. Invoking (l1) it is easy to calculate that the clock cycle is t=\gamma 2L/c, \gamma = 1/\sqrt(1-v^2/c^2). That is the same to say that the clock cycle is slower (\gamma > 1). Being situated in the spaceship and taking it as a null frame will produce the same time interval as a non moving light clock, t’ = 2L/c.

    Now for the million dollar question, is there a way to argue, from a special relativistic point of view, that this clock cycle that we easily understand is the same as a more complex clock cycle connected with other physical processes?

    The answer is embedded in (a1). Assume we introduce a new clock model, and make two copies of this new clock. We test them so that we know both produces the same time intervals. One important observation is that we do not make any assumptions about the internal workings of this new type of clock.

    We then take two copies of each, put one of each in the reference non moving spaceship, and the other set in the spaceship that will be future moving. Sending our experimenter in a direction perpendicular to the rod of his light clock and accelerating him to a constant velocity not known for him. He is only told that he will be in constant motion in the perpendicular direction.

    Two things can happen. If the new clock with unknown internal working continues to tick at the same rate as its stationary counterpart it will start to drift in relation to the light clock. Otherwise there will be no (unknown) drift. Hence, if the new clock is unaffected (that is continue to tick at the same rate as its stationary counterpart) our experimenter can use it’s drift to calculate his velocity in relation to the rest frame violating (a1).

    So we have answered the million dollar question. In a special relativistic frame work, since the introduced temporal process can be unknown, all temporal processes gets slowed down by the same amount. And this must happen if the special relativistic assumption of time dilation is true. That is that local time on the space ship in motion is slowed down as seen from the space ship at rest.

    And to clarify, this says nothing about the physical reality, it says something about the model of special relativity. At least not if one accepts Hume’s problem of induction.

    So, from this, is there a connection to muons?

    Yes, since the mean lifetime of a muons at rest in a laboratory frame is a well defined quantity there is the possibility to do experiments that measure the mean life time of muons that moves with respect to the laboratory frames and look for differences. If the mean life time of muons is a physical process that is connected to time then one should be able to measure an increase in their life time by examining them in motion. If the life time increases one can also compare with the predictions made by special relativity as a model.

    And let me stress, if there is a correspondence, it doesn’t mean that special relativity is correct as a model, it means that special relativity survived that specific falsification test. Any theory that doesn’t should be considered inferior in this matter.

    As a side note, remember that this means that special relativity trivially passes all natural tests of classical mechanics (I here mean conducted in a day to day setting here on earth), and electrodynamics, since classical mechanics is the low velocity limit of special relativity and that electrodynamics also is completely contained in the theory.

    Measurements on muons (and other particles with a limited life time) have been done on several occasions and can easily be found for those who are interested. To summarize, special relativity passes these tests and classical mechanics fails.

    If one is interested in how such an experiment can be set up I recommend the book “Techniques for Nuclear and Particle Physics Experiments – A How-to Approach” by W. R. Leo.

  11. Mike

    Cleas, do you have a reference to a controlled experiment where it is examined if the muon life time gets affected by magnetic fields?

  12. Richard T. Fowler

    Considering how knowledgable you are about special relativity, perhaps you can explain how it is that light can be of constant speed, if the speed of things is dependent on time, and the passage of time is not constant.

    I say it is impossble, and that you cannot prove otherwise — neither with argument, nor with experiment.

    Can two physical things, one light and one not light, interact in the same frame but maintain two different time-speeds at the same instant?

    Would that not result in logically impossible situations, e.g. things being smaller or larger than they are, or events happening before or after they happen, or moving slower or faster than they are moving? Or light and non-light meeting up before or after they do? Or perhaps a ray of light having two different energy levels or frequencies at the same instant and at the same point in space?

    How could that be called science? I don’t even think that could qualify to be called religion. It seems to me that to believe something like that is simply delusion, and nothing more.

    Prove me wrong, if you can. Otherwise, there is really nothing else to talk about, as far as I am concerned.

    RTF

    • Claes Johnson

      The speed of light is by definition 1 lightsecond per second.

      • Richard T. Fowler

        That’s like saying “The height of RTF is one RTF-height per RTF”. It begs the question.

        RTF

      • Richard T. Fowler

        To state more formally, you cannot define a speed as being dependent on a unit of length, when your unit of length is previously defined as being dependent on that very same unit of speed. If you try to do this, then you haven’t defined anything at all. You have a vicious circle in your logic.

        RTF

      • Richard T. Fowler

        Oh, and one other point. You and I don’t get to “define” the speed of an object, whether it be energy or matter. No human being gets to do that. We get to define what we mean by the word “speed” with a physically valid definition, and we get to measure (or at least try to measure) the speed of an object over a period of time.

        But we don’t get to set a speed of a certain object by definition. The speed is what it is, regardless of what we try to “define”.

        If we choose to assume that it is constant for a certain purpose, and it is not in fact constant in reality, then we’re going to have a problem, aren’t we? But even then, that is not a definition. It is simply an assumption. The choice of some to call it a “definition” does not make it a definition. It is what it is, human incompetence notwithstanding.

        It is an assumption. And a very strange one, at that.

        RTF

  13. Mike

    First let me emphasize that I do not consider myself as especially knowledgeable in the field of relativity.

    I have basic understanding on the level of an undergraduate in theoretical physics, nothing fancy at all.

    Second, maybe it isn’t that smart to talk about light speed since special relativity really isn’t a theory about light speeds. It’s better to introduce a concept of a universal speed not necessarily connected to light. That is to say that light may or may not have this universal speed. If not then light has a rest mass. Let us call that universal speed c (I think the discussion will be more lucid if we keep this symbol and don’t care about units, the natural thing is to set c=1).

    Your question (about constant speed) asserts that there is a transformation of time, you do acknowledge a change in time. When we talk about special relativity this transformation is the Lorentz transformation (well, it’s really a Poincaré transformation but that doesn’t change anything).

    Hence we can introduce a Lorentz scalar ds^2 = c^2*dt^2 – dx^2. This is a quantity that is invariant under a Lorentz transformation.

    {
    If the last statement isn’t immediately understood the following can be helpful.

    ds’^2 = c^2*dt’^2 – dx’^2 = c^2*g^2*(t – v*dt/c)^2 – (-v*dt + dx)^2 = g^2(c^2*dt^2 – 2v*dt + v^2*dx^2/c^2) – g^2*(v^2*dt^2 – 2v*dt + dx^2) = g^2*[(1-v^2/c^2)*c^2*dt^2 – (1 – v^2/c^2)*dx^2]=g^2*(1 – v^2/c^2)*[c^2*dt^2 – dx^2] = c^2*dt^2 – dx^2 = ds^2,

    since (1 – v^2/c^2) = 1 / g^2

    }

    So we the value of ds^2 is the same in all inertial systems, ds^2 = ds’^2.

    The natural question is how can we find the value of ds^2?

    ds^2 = c^2*dt^2 – dx^2 = c^2*dt^2*(1 – [dx/dt]^2/c^2)

    So, when the velocity in some inertial frame is equal to the universal velocity, that is dx/dt = c, ds^2 = 0. But this is true in all inertial systems with ds’^2 = 0.

    This gives,

    0 = 1 – [dx’/dt’]^2/c^2, which finally gives us, dx’/dt’ = c, where (‘) indicates any inertial system.

    This should straighten out you question.

    If not, then maybe relativity theory just isn’t for you ;).

  14. Mike

    Ok, maybe the last line sounded a little harsh.

    If my answer is to abstract for you, maybe you can sort it out by trying to understand Feynman’s light clock (I’m not completely sure that he introduced it, but just let us call it that) that is described in the comment above. It should give you a simpler tool.

  15. Mike

    Sorry, there is some typos in the comment above,

    Use the following instead,

    {
    If the last statement isn’t immediately understood the following can be helpful.

    ds’^2 =

    c^2*dt’^2 – dx’^2 =

    c^2*g^2*(dt – v*dx/c)^2 – (-v*dt + dx)^2 =

    g^2(c^2*dt^2 – 2v*dt*dx + v^2*dx^2/c^2) – g^2*(v^2*dt^2 – 2v*dt*dx + dx^2) =

    g^2*[(1-v^2/c^2)*c^2*dt^2 – (1 – v^2/c^2)*dx^2]=

    g^2*(1 – v^2/c^2)*[c^2*dt^2 – dx^2] =

    c^2*dt^2 – dx^2 =

    ds^2,

    since (1 – v^2/c^2) = 1 / g^2

    }

  16. Richard T. Fowler

    You write:

    “Your question (about constant speed) asserts that there is a transformation of time, you do acknowledge a change in time. When we talk about special relativity this transformation is the Lorentz transformation [. . . .]”

    No.

    I do not acknowledge that there is a transformation of time with motion.

    Anywhere, at any time.

    That you cannot see this is just a further example of the delusions that I have been talking about.

    I appreciate your retraction of the harsh statement, but let us be serious here: how can you possibly think that I have acknowledged anything of the sort?? When it comes to the speed of time, I have done the exact opposite: I have relentlessly attacked the idea that time is dependent on motion.

    As far as the light clock, I thought I had made clear with my last comment that your hypothesis implies that if the light has to interact with something that is not light, then all the transforms are immediately rendered moot. Because the hypothesis posits two frames in same place at the same time, which immediately introduces absurd impossibilities. As far as I can tell, your response does not even begin to address that point.

    You are comparing two inertial frames, while I am trying to compare one inertial frame with the universal frame. Your hypothesis implies that the universal frame intersects with inertial frames wherever light is present (which, I suppose, is pretty much everywhere, isn’t it?)

    So if I’m to spend time trying to understand a light clock, don’t I first deserve a coherent summary of how it can work without involving non-light components? And of course, that would be impossible.

    Which would go a long way toward explaining why you don’t give such a summary, i.e., that you really do know the clock does use non-light components, and that this renders the clock impossible.

  17. Mike

    Ok, your original question

    “Considering how knowledgable you are about special relativity, perhaps you can explain how it is that light can be of constant speed, if the speed of things is dependent on time, and the passage of time is not constant.”

    So you ask, how can a speed be constant given

    (p1) speed is dependent on time
    (p2) the passage of time is not constant

    To answer your question I must of course accept the two premises (p1) and (p2).

    I then continue to show that in the framework of special relativity there is one speed that fulfills your question, given the premises and that is the same speed that appears in the Lorentz transformation.

  18. Richard T. Fowler

    I do not see anywhere that you have shown that light can be of constant speed without causing the absurdities I listed. Perhaps you can quote the exact place that you do this.

    RTF

  19. Mike

    Here,

    “0 = 1 – [dx’/dt’]^2/c^2, which finally gives us, dx’/dt’ = c, where (‘) indicates any inertial system.”

    Maybe I should have started the whole discussion with,

    Assume that there is a velocity c that is constant… and so on.

    Maybe it is that step that confuses you? That kind of statement is naturally taken as implicit in the proof.

  20. Mike

    I also want to say that you shouldn’t ponder to hard over the light-matter interaction issue.

    Two reasons.

    First, as I stated earlier, special relativity isn’t really about light signals. They do not need to enter the theory at all.

    Secondly, I personally am not comfortable at all discussing relativistic interaction between light and matter. That must be consider as a hard problem since you need to introduce a quantum field theory for that.

  21. Richard T. Fowler

    Mike, all this proves is that you have assumed that something can have constant speed. You haven’t addressed the absurdities that I listed at all.

    Was this a deliberate omission? If so, then why pretend that you addressed my challenge?

    RTF

    • Richard T. Fowler

      I.e., why pretend that you answered the question you were asked?

      RTF

      • Mike

        Claes should be able to answer that one for you.

        By all means, he is the professor in mathematics… 😉

  22. Mike

    No, it is shown that a constant speed is consistent with special relativity, nothing more nothing less.

  23. Mike

    I interpreted your original question as how a constant speed can be possible at all.

    You should restate your question in a more lucid fashion otherwise.

  24. Richard T. Fowler

    I thought it was quite clear, but I’ll restate.

    How is it possible that light can have a constant speed across all reference frames, within any model that assumes your p1 and p2, and not cause the absurdities that I listed?

    RTF

  25. Mike

    You need to be more lucid about your assumed absurdities to.

    I think that I addressed them earlier.

    “I also want to say that you shouldn’t ponder to hard over the light-matter interaction issue.

    Two reasons.

    First, as I stated earlier, special relativity isn’t really about light signals. They do not need to enter the theory at all.

    Secondly, I personally am not comfortable at all discussing relativistic interaction between light and matter. That must be consider as a hard problem since you need to introduce a quantum field theory for that.”

  26. Mike

    Basically you try to argue that special relativity is inconsistent because it uses a universal velocity.

    I do claim it’s clearly shown that this inconsistency doesn’t exist.

    I do think that Claes will back me up on this.

  27. Richard T. Fowler

    So Mike, is that your answer is that we know no absurdities of the type I mentioned are introduced by a constant velocity of light, because light-signals do not need to enter the theory? But doesn’t that then imply that anywhere there is light, the theory is disproven?

    RTF

  28. Mike

    Then you need to be more explicit by what you consider the absurdity to be.

  29. Richard T. Fowler

    I need to be more explicit?

    You mean more explicit than this:

    “e.g., things being smaller or larger than they are, or events happening before or after they happen, or moving slower or faster than they are moving? Or light and non-light meeting up before or after they do? Or perhaps a ray of light having two different energy levels or frequencies at the same instant and at the same point in space?”

    You mean that there is some ambiguity in that?

    Or do you mean that the question is somewhat disquieting to consider, and you’d rather give me busy work improving the specificity so you can avoid trying to answer?

    RTF

  30. Mike

    Do consider my second objection.

    I really don’t see how wee could have a discussion here about how a spin 1/2 spinor field can couple to a spin 1 vector field.

    I don’t think I could give the arguments proper justice in a forum like this.

  31. Mike

    Aha, I think I know what you mean.

    You get hung up about the standard apparent paradoxes in the theory.

    You know what you should do, you should read up on that in a introductory text to the subject. The most common “paradoxes” are explained in them.

    I will see if I can recommend some suitable book for you.

    • Richard T. Fowler

      As regards your statement,

      “Secondly, I personally am not comfortable at all discussing relativistic interaction between light and matter. That must be consider[ed] as a hard problem since you need to introduce a quantum field theory for that.”

      If you need to introduce a quantum field theory to save SR from apparent paradoxes, then SR falls. It is known that quantum “theory” and Einsteinian relativity are mutually exclusive.

      If I say to you,

      1. Model A shows that the roof of this house can be held up by the walls, and shows how.

      2. Model B shows that the walls of this house can be held up by the roof, and shows how.

      and then you show me a catastrophic problem in model B, I cannot save B by appealing to the techniques of A, because we know that both A and B cannot be simultaneously true.

      RTF

      • Mike

        No, there is no need to introduce quantum field theory to resolve the paradoxes. I thought that you got hung up on light-matter interactions.

        Secondly there is only the general relativity theory that is incompatible with a quantum field theory, and that is only in some extreme regimes. That is to say that they get along quite good until you start to look at really extreme events.

        A basic quantum field theory is a quantum theory in a special relativistic setting. No more, no less. But you can formulate quantum field theories in a curved space-time to, no problem at all.

      • Richard T. Fowler

        My objection to light-matter interactions is included in both of my points. But on this specific point, I raised it because I believe your “clock” is impossible, whether or not it would use non-light components.

        RTF

  32. Mike

    Question for you Richard.

    What kind of math are you comfortable with. Calculus? Complex calculus? Vector algebra?

    • Richard T. Fowler

      I struggle with all of those, but what I would like to hear is the simplest answer that is fully responsive. If I can’t understand it, then I’ll work on it until I can.

      But if, once I understand it, I find that you were blowing smoke the whole time, don’t expect me to be happy about it.

      RTF

      • Mike

        Ok, that is far from optimal, but maybe not impossible.

        Would you say that you understand why ds’^2 = ds^2 in the derivation above?

      • Richard T. Fowler

        No, quite the contrary. My understanding is that ds’^2, by definition, cannot = ds^2 if s is in the universal frame and s’ is in a moving inertial frame. If, on the other hand, you define time as constant across all frames and allow c to vary, then I suspect we are getting closer to reality.

      • Mike

        I meant do you understand from a mathematical point of view?

      • Richard T. Fowler

        If you mean can I follow exactly what the derivation is trying to say, on a good day, if I go slowly, I can. But this is not the best day right now, so just assume that my knowledge of the details is limited, and say what’s on your mind. I promise I’ll give it a thorough study, and if it makes sense, I shouldn’t have any problem picking that fact up.

        I think that if the answer to this problem is as simple as you’ve suggested, it shouldn’t require extensive math to summarize. But if you want to write it all down, feel free; I won’t complain. The answer is equally meaningful (or meaningless), whether one expresses it with math or other language. And I accept the responsibility of decoding math (in my own time), if that’s how you want to give it to me.

      • Mike

        I must admit that I’m having a hard time formulating what I want to say not using math.

        Maybe the best thing you could do is examine some wikipedia pages.

        Try to understand “the Ladder Paradox” for instance

        http://en.wikipedia.org/wiki/Ladder_paradox

      • Richard T. Fowler

        There is a ladder and a garage in that paradox. The ladder is moving faster than the garage, and is thus said to be able to fit completely inside at one moment. But this involves three frames: one for the ladder, one for the garage, and one for the universe. In the universal frame, the ladder cannot fit inside, no matter how fast it goes.

        But that is not what we were talking about. We were talking about light and matter, in a frame where all the matter being considered is in the same frame. Different problem. But I do very much appreciate your trying to help. Maybe it has helped you some, too?

        RTF

      • Richard T. Fowler

        By the way, this brings up a story that may interest readers. I had honestly forgotten about this until just now, since I posted the previous comment.

        My first exposure to the ladder paradox was at the age of 10. I am now 36.

        I was in an advanced program in a small school, and our science class was taught by a woman named Brooks Mitchell, whose expertise was in child psychology and educational theory. She was the principal of my school. The science class contained about eight of us, with an age range of about 9 – 12.

        So Mrs. Mitchell was trying to introduce to relativity theory, and this paradox was one of the tools she used to do so. I recall that at first, there was no comment from the class. But after, maybe 2-3 minutes of studying what we had been offered, I started giving here the full monty, more or less what I’ve doing to Mike today. Basically, I was saying it made no sense as presented, and therefore I wasn’t buying any of this so-called “relativity theory” unless she could somehow fix the paradox. But, not surprisingly, she hadn’t thought of the problems I raised, so she had no fix to propose. In the end, she admitted that I may be right about relativity “theory”.

        After that, she used to tell me (and others) that I would make an excellent physicist, but I was always confused by this, because I already knew that my grasp of math was not where it had to be. But then again, perhaps under the circumstances, that was a saving grace for my understanding of physics.

        As far as I can remember, I have never once given any serious attention to the ladder paradox again, until now. I had seen fleeting references to it, but I had quite forgotten having studied it in grade school. Now I’m glad I did — even though it was frustrating having that stuff about relativity thrown at me and being told that it was basically it was the state of the art of physics! I remember clearly getting all chilled with anxiety before I spoke up, because it seemed so obvious at the time that it was total refuse, but I wasn’t sure I could clearly express what was wrong with it. At the time, of course, I had no understanding of the universal frame, so I wasn’t able to explicitly refer to it in my objection. But I just kept repeating over and over, words to the effect of, ‘But that’s only from inside the garage! From the perspective of outside, it’s different! Why isn’t the paradox mentioning that?’

        True story, as best I can recall. As God is my witness.

        RTF

  33. Mike

    If I understand you right Richard it’s these kinds of questions that you feel muddles up the relativistic theory:

    “e.g., things being smaller or larger than they are, or events happening before or after they happen, or moving slower or faster than they are moving? Or light and non-light meeting up before or after they do? Or perhaps a ray of light having two different energy levels or frequencies at the same instant and at the same point in space?”

    You are basically wondering about stuff like causality violations.

    If you want to understand why these types of question isn’t a problem in a special relativistic framework there is no short route to do it. You need to roll up your sleeves and get your hands dirty so to say. You need to work through different types of paradoxes and understand why there is no paradox. This is easiest done with a fair amount of math but could surely be done using a minimum of math I guess. At first glance it looks like wikipedia (not just the ladder paradox, there are links to several) takes this approach.

    But don’t despair, I know that relativity has a reputation of being hard to understand. I think that is unjust when it comes to special relativity. It do takes some time to get used to, and one has to be ready to work on understanding it. But it is not intrinsically especially hard to understand, and there is no complicated math involved. A relatively (pun intended ;)) long proof in functional analysis based on topology for instance is much tougher to understand.

    My guess is that your biggest problem in understanding this is that you try to mix what relativity says with your own thinking on how the world should behave.

    One of the best qualities in theoretical physics (or science in generally) is to be able to drop ones personal biases when trying to understand a new theory. That doesn’t mean that you must stop believing in what you believe.

    Let me try to set this in context based on the ideas of Thomas Kuhn’s philosophy of science.

    Philosophy of science, as you may be aware of, has one huge question.

    ‘What is science and what is pseudo science’.

    Answering this is called the Demarcation problem, where is the border that demarcates scientific theories from non scientific ones.

    Unfortunately I’m running out of time, but I sure like to continue.

    Maybe this is a good place to pause to, because for now I can’t find my copy of Poppers ‘The Logic of Scientific Discovery’ for now and we need him on the step to Kuhn’s ideas. 🙂

  34. Richard T. Fowler

    Mike,

    My objections have nothing to do with my biases about how the universe should be. The universe is what it is, and I know that honest observation will reveal much about how it is. My objections stem more from the risible idea that scientists can be objective, i.e. unbiased. THEY CANNOT. We live in a fallen, corrupt world, and our bias is a reflection of that fallen, corrupt state.

    All we each can do, from a scientific perspective, is do our best to observe, and do our best to interpret the reports of others, and do our best to reason as to what all the results suggest and/or imply. But look here: in doing this, we have to not only try to minimize our own bias … we also have to take account of the non-zero bias in the others whose work we are considering.

    By failing to do so, we can condemn ourselves to endless running in rhetorical circles and accomplishing nothing of value.

    I’m quite familiar with Kuhn’s ideas. I got an A in history of science as an undergrad. But that is immaterial to what we are discussing. We are discussing the “theory” that you have been trying to defend, which its own author and many other mathematicians and physicists who have worked with it and have purportedly used it to make predictions freely admit has no physical reality. But you will not consider their objections; you reject them out of hand. So it seems that you are the one who has the unreasonable bias here.

    I showed up at Frank Davis’s website in December 2010, believing fully in Einsteinian relativity, and frankly not very aware that there were serious objections to GR which amounted to accusations of fatal flaws. I saw Frank openly questioning quantum physics, and quoting others, and was amazed at how in-depth the arguments were. But I still considered the arguments to be probably false. I had, at that point, a bias in favor of the standard model, which bias I was well aware of, and which I hadn’t felt necessary to do anything about.

    At the same time, I was convinced (not through bias, but through hard research) of the reality of much physics being kept classified, but I was not aware that this impeached mainstream relativity concepts in any way.

    Regarding doubts about quantum physics, I asked a few questions of others within an Earth-science context, and came away with slightly more skepticism about the standard model, but my skepticism about it was still tilted more toward quantum concepts. I just didn’t understand either those or GR well enough to have what I now know to be the right point of view.

    It wasn’t until this past November, nearly a year later, in reading Claes’ work, that I finally understood many of the points that I am making now. Claes explains things that others simply fail to. And that is not just bias talking; that is the cold, hard reality.

    So it doesn’t surprise me in the slightest that he is being attacked professionally. In fact, I’d be dismayed (and not a little suspicious) if he weren’t.

    You talk about bias; with all due respect, unless you’ve studied conspiratology professionally, I don’t think you can truly know the meaning of the word “bias”. You go out and make a career out of that, sir — whereupon you will witness many threats (or worse) made on your life and/or those of your loved ones — and then you are qualified to speak intelligently about what is an unreasonable bias and what is a profoundly reasonable one. From your words, it is clear you haven’t made the career choice I allude to, and are not close to anyone else who has.

    Thus, for you, everything you’ve read about it can be analyzed in a cold, “objective” way, far removed and safe from the threats, the attacks, and the homocides that were endured to bring you that information. In such a situation, it is like you are living in a bubble — in your own frame, so to speak. You think you know bias, and you think you are a good judge of it in other people; but the word has different meaning in your frame than it does in mine, and in others’. You think you are disputing scientific matters, but you are really disputing religious and political ones; and we all know that genocide is an all-too-common feature of such disputes. That’s why everyone in this conversation is all on eggshells. It’s not so much about credit or professional reputation. It’s about that word that hangs over all our heads, that hangs in the air, that most everyone senses at least occasionally, but that nearly everyone who is consciously aware of it is afraid to utter aloud. People have been killed over much, much less than what you and I are talking about right now — and talking right out in the open! With over 300 page-views a day. I guarantee you you have a much more significant audience right now than you had realized. That is not a warning to you, because I don’t think it likely that you are in any danger. But it is intended to try to suggest that if my words sometimes don’t make sense to you or seem half-baked, it may just be because I am not always at liberty to fully explain myself — not because of some perceived bias against the hypothesis.

    The hypothesis falls based not on bias, but on its own internal inconsistency. I have already shown that, and Claes has as well. I find it interesting that you accuse me of bias, since you have admitted on this same page that SR depends on quantum physics for its defense, and you admitted on another page that SR depends on assumptions of GR for some of the consistency that it does have, and you admit on this page that GR is mutually exclusive with quantum physics — but you will not admit that these three facts together make SR and quantum physics mutually exclusive, which makes SR impossible, because to be true it would have to simultaneously accept and reject quantum physics. That is internal inconsistency. That is self-contradiction right there. And you apparently cannot see it. So where does the real bias lie?

    I also find your accusation of bias interesting for another reason: since the hypothesis tries to claim that it can somehow justify the idea that a given event simultaneously occurs at one moment, and at more than one moment, which, the only way it could do so is by blowing more smoke to cover up the old smoke. So, since logic tells me this, I don’t need to see Popper and I don’t need to the math that supposedly does the trick, and I don’t need to see any more experimental results. None of that can possibly deal effectively with the internal inconsistency, with the self-contradiction, which is openly admitted every time a defender of SR says something like, “this is just a manner of looking at it,” or “it’s just an appearance, not reality” or “this is just the inertial frames, not the perspective of the universal one”. These are all the functional of saying, “The theory is not true”, which is the functional equivalent saying, “The theory is not a theory”, which is a tautology. It would be true if we put the first one in quotes: The “theory” is not a theory.

    I would argue that it would be untenably biased not to make these characterizations.

    I’ll illustrate with an example. I have a cat on my desk. She is lying on my wife’s sweater, because she likes the extra warmth that she gets from doing that. She has been doing this very often recently, so that the sweater is covered in a thick mat of cat-hair. But she’s all right with that.

    If I were to look at the cat and, God forbid, say, “I doubt that you exist”, which I would never do, I would be committing a tautology. By saying that the cat does not exist, I am saying the functional equivalent of: This cat is not a cat.

    That might be acceptable if I know that I have had hallucinations of this particular “cat” before, and that they are just that — hallucinations. But even then, I have to put the word in quotes: This “cat” is not a cat.

    But if I have raised the cat from kittenhood … if many of my family and friends and neighbors know the cat, and interact with her … if I’ve been feeding and cleaning up after her for years, and having to rearrange my life to accommodate her needs … then it is not “biased” to claim that the cat does exist, that she is not just a “cat” with quotes. In fact, it would be “biased” not to.

    (For the record, I do not have chronic hallucinations. That was just a thought experiment for educational purposes.)

    Some things you can have doubt about. Some things it would be unreasonable to have doubt about. Some things … you cannot doubt, even if you might want to, because they’re in your face, filling up your senses with non-self-contradictory information. So when someone tells me I am biased for believing that thing, what kind of reaction do you think I would have to that? “Oh, thank you kind sir, what would I do without you to set me straight? Of course 2+2=5! What could I possibly have been thinking?” Or, something else?

    In conclusion, I think the best use of your time with respect to this question is to just get your textbook, copy the math out, and post it here. Let me and others judge the validity of it, or lack thereof. Don’t bother with the philosophy; based on what you’ve already posted, I can assure you that I have had a much more open mind about all this than you have. And it really does jar me to be told otherwise. The only reason it may appear otherwise is because, for all my confidence, even I don’t have the sheer audacity to lecture you that I’m perfectly objective, and that the only problem here is that you have bias.

    RTF

  35. Mike

    Richard,
    you seem to get upset, that was newer my intention.

    I simply meant biased in the meaning,

    ‘Bias is an inclination to present or hold a partial perspective at the expense of alternatives’.

    We all do it. For all I’m concerned there is nothing shameful or bad with this, it’s human nature.

    My point was that to understand the implications of a theory, in a theoretical setting, you need to assume that the basis of this theory is true. As long as you don’t do this you will never understand the theory. It may lead to absurdities and that must be ok.

    You are certainly right, everybody has some bias. When doing science it is very important to publish your work so that others, working in the same field, can examine your work and comment on why or why not your work holds up. You can never judge yourself if you are being objective or not and there is a lot of tests in clinical psychology that says the same, hence you really need the collaboration of others.

    I repeat my earlier statement that if you want to understand this theory you need to roll up you sleeves and get your hands dirty, the understanding has to be done by one self. Otherwise it is like saying, I need to pee, can you do it for me.

    As I, at least vaguely, pointed out earlier, I’m not completely sure that you can understand these concepts without math. I’ve pointed you in a possible direction, the Wikipedia articles. If you are genuinely interested in understanding this theory I think that can be a good start.

  36. Mike

    Maybe I should clarify according my own stance.

    Do I claim that special relativity is proven true, no.

    First of all, according to the knowledge of today special relativity can be no more than an approximation.

    We also have to consider the problem of induction, next week they may do a measurement of some anomaly at LHC, or some place else, that forces everybody to reconsider all fundamental understanding up till date.

  37. Mike

    I am looking into the Many Minds Relativity text, but it’s a slow read. I much would prefered if it was written in a short and concise manner.

    I have question to Claes regarding this text.

    Can there be excluded that the standard formulation and your many minds formulation isn’t equivalent?

  38. claesjohnson

    They are far from equivalent. Newton’s 2nd Law takes different forms, for example.

  39. Mike

    Then one should be able to evaluate the many minds formulation against the standard formulation using accellerator experiments.

    Collissions should not happen in the same way in the two different formulations.

    Do you agree or disagree?

  40. Mike

    To clarify,

    if the form doesn’t matter and the two different formulations is consistent with high velocity accelerator experiments, then they are equaivalent in this respect.

    But if they differ one can see wich theory is consistent with high velocity accelerator experiments.

  41. Mike

    One more question Claes.

    Have you evaluated what symmetries and charges the many minds formulation generates?

  42. Daniel

    What is the t in Newtons equation?

  43. claesjohnson

    t is time as measured by a standad atomic clock.

  44. Daniel

    Ok, because I was reading about many minds relativity and you state on page 158

    m1, all observers share a common time,

    is this a definition?

  45. Daniel

    Oh, yes of course, I also meant to write that I think this is exactly how Newton thought about it. That there is a common time shared by everyone.

    That’s the thing that puzzled me for a long time, if this is a definition or not.

  46. Mike

    That is a really good question.

    There seems to be a predicament here.

    To indroduce an absolute time does seem to need the requirement to do it by definition.

    The time in the definition is absolute since a cycle of a cesium clock must be invariant for all observers. Otherwise they doesn’t measure a common time.

  47. claesjohnson

    A cesium clock works the same for all observers in inertial motion, and thus sets a common rate of time which is the only thing entering in the equations of motion as a common time step “dt”.

  48. Mike

    Can you show that with an experiment, that the clock works the same for all observers in relative inertial motion?

    Or do you have to define it?

  49. Richard T. Fowler

    As I have suggested before, I think it is reasonable to suppose that time is variable. but as I cannot conceive of any way to effectively model space with both variable time and variable c, I think it is most reasonable to set it as a constant. That is not the same thing however, as trying to define the speed of an object, which is something that can be measured (how precisely is another question, and thus which it would be invalid to try to define. Again, it can be set by assumption for a certain, but to try to define the speed of an object is not scientific, because it ignores that the object has a measurable speed.

    Time, it seems clear, has a speed (whether variable or fixed is immaterial, it has a speed). However, since one reasonably cannot measure it without assuming a fixed speed of something else, and since there is not reasonable basis to assume that the speed of anything else is fixed, it must follow that that one reasonably cannot measure the speed of time. Therefore, it must be considered valid for modeling purposes to define it as having constant speed. Note that the definition I suggest is not of a value of speed, which could not be considered scientific, but simply of the word “time”. The definition would state that time is a constant of unknown quantity, which is related to certain other known variables by certain functions which introduce an assumed range of possible values for each variable, in relation to both time and to one or more of the other variables. This of course brings in the necessary issue of forcing, which would apparently have to be addressed as part of one’s definition of time.

    That is how I would approach dealing with this problem.

      • Richard T. Fowler

        I should also point out that I don’t believe that extra-universal time varies, and if it does, so what? What we are really concerned with is how intra-universal time relates to extra-universal time; if it varies directly, then we can consider intra-universal time to be “constant” and include such a restriction in our definition of “time”; if it does not vary directly, then that would correspond with variability in our definition of “time”.

        See, Claes, it’s as I told you: it’s really impossible to give a thorough consideration to matters of cosmology without involving religion or, if you prefer, articles of faith. The difference is, I admit it, and most scientists can’t or won’t — even though they end up working with such matters anyway.

        RTF

  50. Mike

    Yes Richard, l think you could think of a time defintion where time has a “speed”. That’s kind of what Claes does. He defines a time with constant “speed”.

  51. Mike

    Come to think of it, the natural way of defining a velocity in special relativity is a four velocity.

    It behaves in such a way that the speed of it is equal to c, the universal velocity.

    In this view you (yes you 😉 ) have a constant speed through space-time and it is equal to c.

  52. claesjohnson

    Mike: It is inconceivable, impossible, unthinkable that a clock, a mechanical or quantum mechanical periodic system, can be be affected by pure translation with constant velocity (inertial motion). Anyone questioning this fact must come up with a reason that the mechanism of a clock can be influenced by inertial motion.

  53. Mike

    How do you show it experimentally Claes, with another clock?

    I’m not saying it is this or that.

    You claim that it is in a certain way.

    Is this claim by definition or is it a provable fact?

  54. Richard T. Fowler

    Claes, I agree.

    Mike,

    Yes, well that’s why I brought up forcing between the variables that are related to time by definition in a model. If the definition of time does not make reference to the magnitudes and directions of those forcings, then all you end up with, for your effort, is a meaningless, pure mathematical translation that lacks any measurable physical effects.

    RTF

  55. Richard T. Fowler

    Mike,

    To clarify, I am not trying to relate the speed of either time that I mentioned to space compression or extension. I am trying to relate speed of intra-universal time to the motion of specific objects or classes of objects. This can be tested experimentally, but only by comparing two different objects simultaneously, for example, a ray of light and a sample of cesium radiation. But since the speed of these multiple objects will not necessarily vary directly, it only makes sense to set time speed as a constant of unknown value, and then approximate that value by averaging the measured relative speed of several different objects (i.e., relative to each other, and assuming that space is not expanding or contracting during that time. (The volume of the universe may be assumed to be expanding, without causing any expansion of space itself.)

    RTF

  56. claesjohnson

    Mike: Yes with two clocks in two inertial systems. In order for the clocks to tick at different rate, there must be some mechanical reason that they do so. No such reason is known, and therefore there is no reason to assume anything but the same rate of time for both clocks. Give a reason or quit arguing without reason.

  57. Mike

    How would you construct the experiment?

    Or you should state what kind of conditions you consider to be reasonable to perform such an experiment.

    You formulate the theory, so either you define the things you introduce or you give an experiment that justify you assumption.

    I say the predicament still holds.

  58. Mike

    By the way Claes, you asked about a mechanism that would affect the time measured by clocks.

    Isn’t that a bit unimaginative?

    If there is a universal constant velocity, one candidate would be the speed of light, you have your mechanism.

    Look up the Feynman light clock if you haven’t done that already, its up above in one of the commentaries to this blog post.

  59. Mike

    Ok, I apologize for the ‘unimaginative’, I’m riding out a flue and feeling a bit irritable. So I apologize once more.

  60. Mike

    Claes you have been given a reason.

    Now, is your statement about time a definition or not?

    And if not, how do you determine that the statement is true?

  61. claesjohnson

    I have seen no reason that inertial motion will influence clock rate. What is the reason you speak about?

  62. Mike

    Did you read the discussion about the light clock which shows one mechanism for the slowing of a clock that is in constant motion relative one stationary observer?

  63. Mike

    Let me just check up with you, is there anything with the light clock that you think is unclear?

  64. claesjohnson

    What is a light clock? I know what a mechanical clock and an atomic are, and these are the only clocks I know as being useful in science.

  65. Mike

    (1) A clock must reasonably be manifested by any physical system that can be used to measure temporal progression. Do you agree or disagree? If not, why?

    (2) Any physical system with a well defined periodic behavior could then be used as a clock, do you agree or disagree? If not, why?

    (You could also use a physical system with a well defined start and well defined end, for instance the life of decaying particle, but this is for now a side point)

    If you affirm to this two statements (if not you should elaborate why) the following earlier comment applies.

    https://claesjohnsonmathscience.wordpress.com/2012/01/27/questioning-relativity-definition-vs-axiom/#comment-741

    I do think I see a resolution to the predicament, but first I’m interested to see if you could find the resolution yourself.

  66. Mike

    Wow, that was not pretty at all.

    Isn’t it some way so that comments could be previewed?

    Well, the information is still the same.

  67. claesjohnson

    There is a SI standard clock which is a Caesium clock and this is the only clock there is. All clocks have to be synchronized with the standard clock. It is unthinkable that a Caesium clock can be affected by inertial motion.

  68. Mike

    So you want to define time as a measurement from a cesium clock?

  69. Mike

    Better up.

    Can you tell us why you disagree with (1) and (2)?

  70. claesjohnson

    This is the adopted standard, not my personal conception.

  71. Mike

    What is your personal conception then?

  72. Richard T, Fowler

    With due respect, both of you are engaging in circular argument.

    You propose to test the proposition that time does (Mike) or does not (Claes) vary with motion.

    In either case, you are starting with the assumption that it does not vary without motion. This, as I have said, is a reasonable assumption, even if it may be false. It is reasonable because modeling the alternative seems too difficult.

    You both then implicitly assume that there exists one or more objects (e.g. caesium radiation, light) that travel with constant speed. The suggestion, apparently, is that experiment has already shown this to be a valid assumption.

    How did experiment show this? If it was by comparison to another moving object, then it would be necessary to show that that object moves with constant speed, in order to test the first object. To test the second object would require an experiment comparing it to a third object, and so on, ad infinitum.

    So, assuming this validation has not been done (since it would appear to be impossible due to infinite regress), it must then follow that it is simply being assumed that your respective preferred object moves with constant speed.

    If this assumption is true, it implies that time cannot vary for that particular object.

    If time cannot vary for that object, then it cannot vary for that object within any inertial frame, nor in any non-inertial frame. I.e., it cannot vary for that object in any frame where that object would be found.

    If time cannot vary for that object in any frame where that object would be found, then it cannot vary for any other object in the same frame. Therefore, time cannot vary FOR ANY OBJECT between two frames that both contain the control object.

    So as can be seen by the above, the experiment begins with an assumption which implies the question that is supposed to be tested. The experiment is begging the question.

    I sincerely hope you will both take this very simple line of reasoning to heart and apply it to your future comments about this matter. This is not a trivial point I am making. It would seem to be foundational.

    RTF

  73. Mike

    I left a comment under your latest post (Questioning relativity # 20) that I think is of heaviest importance.

    For some reason it didn’t appear in the global list of recent comments, so I thought I mention it here since I think it is very important.

  74. Richard T, Fowler

    I have a comment in moderation before Mike’s #882, on this page. Mine is #880.

    Maybe it went to moderation because I used a bold and then a slash-bold tag to try to get rid of the boldface.

    RTF

  75. Mike

    Taking one step back and looking it has now become clear to me that this whole discussion has evolved into some bizarre meta-discussion that has nothing to do with physics.

    It seems that Claes at least, I’m not completely sure about you Richard, consider physics to be something it is not.

    Physics is not theories that explains the nature in any sense, physics is theories that try to describe nature using mathematical models.

    I do know that there are sometimes grandiose claims about fundamental this and fundamental that, that’s completely besides the point. Just because some “misbehave” do not invalidate the whole field.

    From Wikipedia:

    “Theories in physics
    In physics the term theory is generally used for a mathematical framework—derived from a small set of basic postulates (usually symmetries, like equality of locations in space or in time, or identity of electrons, etc.)—which is capable of producing experimental predictions for a given category of physical systems. One good example is classical electromagnetism, which encompasses results derived from gauge symmetry (sometimes called gauge invariance) in a form of a few equations called Maxwell’s equations. Note that the specific theoretical aspects of classical electromagnetic theory, which have been consistently and successfully replicated for well over a century, are termed “laws of electromagnetism”, reflecting that they are today taken for granted. Within electromagnetic theory generally, there are numerous hypotheses about how electromagnetism applies to specific situations. Many of these hypotheses are already considered to be adequately tested, with new ones always in the making and perhaps untested.”

    Handen på hjärtat (to be honest) ,

    wouldn’t this explain allot of the current confusion in the present discussion?

  76. Mike

    To clarify my last comment,

    I think that we on a meta-level, are not discussing the same subject.

  77. Mike

    Richard, saw that you wrote this,

    “If this assumption is true, it implies that time cannot vary for that particular object.”

    You are spot on. In relativity theory (the model or what you would like to call it) a mass-less object that travels with the constant speed has a proper time (defined as the time that a moving object measures) of zero, that is no experience of time.

  78. Richard T. Fowler

    As far as I am concerned, all we have been discussing, broadly speaking, is what are the relative merits of different models as far as their ability to accurately describe space, time, matter and energy.

    I do believe that that question has significant overlap with physics, as well as with other fields of inquiry.

    RTF

  79. Mike

    “As far as I am concerned, all we have been discussing, broadly speaking, is what are the relative merits of different models as far as their ability to accurately describe space, time, matter and energy.”

    I’m not so sure about that.

    It hit me earlier that Claes reasoning about how Einsteins relativity should be consider as pseudo-science could also be applied to Newtonian mechanics (since there is a metaphysical assumption about time). That’s complete nonsense and can be “resolved” by acknowledging that both theories are just that, theories, mathematical models or what ever you wish to call it. You have to postulate some basic axioms that can’t be proofed within the theory.

    Newtons theory fixates time by assuming it to be absolute, there is an excellent discussion about this using fibre bundles in Roger Penrose excellent book “Road to Reality”, chapter 17. Einsteins theory fixates a universal velocity c. Penrose book also discusses, using fibre bundles, how Newtonian space-time and Einsteins space-time is closely related were it not for the universal velocity.

  80. Richard T. Fowler

    I haven’t gone back to look, but my recollection is that he was calling “pseudo-science” not because of metaphysical assumptions (though based on other statements of his, I think it is possible that he also believes that) but rather because of lack of any physical content or physical meaning of certain elements, including the Lorentz transformation. And Claes is hardly the only researcher to do this. Many physicists, including Einstein himself, have done so.

    Claes has written pages and pages about this subject, approaching it from many different directions. To try to summarize all of that criticism with the words “SR is pseudo-science because it makes a metaphysical assumption about time” is not fair, in my view.

    ‘Nonphysical definitions related, in part, to time’ might be a little bit closer. But it is still a gross oversimplification of his criticisms — partly because it ignores the various ways he has shown internal inconsistency.

    SR is not just a theory that “misbehaves” once it is put into motion. By being internally inconsistent with its assumptions, and by requiring circular arguments to attempt to resolve the inconsistencies, SR establishes itself as, at best, a nonsensical, tragic, and untestable error that should never have been taken seriously. I say “untestable” because, if it were somehow possible for all the postulates and definitions to be simultaneously true (which it is not), there would be no way to observe the effects that it predicts.

    Even if the space I occupy were getting stretched or compressed right now, without any forcing factors between parameters there is no perceptible physical effect, and thus nothing for physics to measure. Therefore, anything that physicists “think” they have measured is something else altogether. Not an effect of SR.

    RTF

  81. Michael

    I would like to bring the discussion on the physics, if this is possible.

    The two Mike’s spacecraft A and B must be equipped with identical devices for the measurement of time if you want that both understand what is happening on the other spaceship wherever it is.

    Each device consists of:
    i) a clock (no matter what kind is it) that beats time local with the period T;
    ii) a system that uses the output signal of the clock to trigger a counter of the local time and that simultaneously sends the signal via radio to the other spaceship;
    iii) a second counter triggered by the signal received by radio that measures the remote time as it is viewed by the receiving ship.

    Scenario 1: A and B are close each other.
    All the counters, once that have been simultaneously reset, measure the same time.
    Scenario 2: A and B have moved and they are far S and both at rest.
    There is:
    LocalTimeA(LTA)=LocalTimeB(LTB)
    RemoteTimeA(RTA)=RemoteTimeB(RTB) < LTA and LTB
    LTA-RTA=LTB-RTB=S/c where c is the light speed
    Scenario 3: A and B are moving away with the velocity v.
    Let consider two consecutive ticks of time spaced T between them.
    The first radio signal (emitted at the time t1) is received at the time t’1=t1+S1/(c-v) and the second (emitted at the time t2=t1+T) is received at the time t’2=t1+T+(S1+vT)/(c-v). That’s the remote time is received whit the period T’=t’2-t’1=T(1+v/(c-v))=T/(1-v/c)

    In other words the time on the other spaceship, as it is viewed by the other or better as it appears to the other ship, passes more slowly. Notice, “nihil sub sole novi”, that is the well known Doppler effect that is continuously experienced in many ways.

    So, the time dilation is really observed but it is an apparent effect produced by the distance and the relative velocity which vanishes when the two space shifts come back close each other. It is the same thing of a body that appears smaller when observed from a distance and returns at the previous dimensions when observed by near. You know well that it really maintains always the same dimensions.

    The time and the space are absolute. They can appear distorted when observed/measured using the light (in general the EM waves). It is well known that the light makes other jokes as, for example, the virtual images.

  82. Richard T. Fowler

    Michael,

    Without having examined existing experiments, I would assume they already take account of any expected Doppler effect. And the same adjustments could easily be done with Mike’s experiment, and with yours. The important point, I believe, is that Mike is claiming that a residual effect would be observed due to alleged effect of SR. His believe seems based on the fact that some other experiments have shown effects that he believes consistent with Lorentz transformation of space and time. His interpretation is falsified by much other evidence — though I admit I do not have all the answers, the non-physicality of his interpretation is self-evident based on a number of different lines of reasoning that have been presented already.

    I have been discussing this further with him at my blog. I am trying to slog through all of the issues he has raised so that I can do another post at my blog about it. I’ve taken a few days off to collect my thoughts. Actually, I think I have gotten him thinking, too, about some things that may not have occurred to him before.

    While I do not agree with Claes’ latest comment on this page, I still think he deserves much credit for his work to educate and re-orient others including myself.

    I do appreciate your thoughts above, as well as your apparent change of mind about Einsteinian relativity. Welcome to the realm of reality! Now, doesn’t it feel better?

    RTF

  83. Michael

    Richard,
    I have never been a supporter of Einsteinian relativity. My first post simply argued that the time dilation is real and, since I am an agnostic, I wondered what could be its cause.
    After reading and thinking a while on the subject I have seen that the dilation of time is compatible with the Galilean transformation taking into account the delay with which an event is perceived by an observer who is far away in space relative to it, since the information is traveling at constant speed.
    A further consideration.
    In my opinion the Einsteinian relativity is based on a completely wrong interpretation of the Michelson’s experiment in which the receiver of the light beam is stationary relatively to its emitter. Therefore the assumption that the speed of light is not affected by the speed of the emitter is completely unfounded and merely hypothetical. That’s, we are faced with a simple syllogism and we cannot make the mistake of confusing the reality with a conclusion logically consistent with the hypothesis.
    We have a saying in such cases: “if my grandfather had wheels, he could be a train”, but who can never think that this may be true!

  84. Michael

    Making right.

    Therefore the assumption that the speed of light is not affected by the speed of the emitter is true only if the relative speed is zero and such assumption is completely unfounded and merely hypothetical if the relative speed isn’t zero.

  85. Richard T. Fowler

    Michael,

    Very well, I stand corrected regarding your previous position. Thank you for your contributions!

    RTF

  86. Michael

    I just read “Many-Minds Relativity” and I realized that perhaps I’d better do it before posting my thoughts.
    I like to see that apparently I’m not the only heretic.

  87. Michael

    Claes,
    at page 156 of MMR you writhe:

    “Concerning (o1) we recall that by the classical Doppler shift, a light signal
    emitted at unit frequency from a source moving with velocity v with respect
    to an observer, assuming that light propagates with unit speed in a vacuum
    at rest with the observer, is received by the observer at the shifted frequency
    f = 1/(1 + v) (14.1)
    The Doppler shift gives a red-shift in recession (with v > 0) and a blue-shift
    in approach (with v < 0). We understand that for v < 0, we have to enforce
    the restriction -1 1, that is a speed
    larger than that of light.”

    I would like to point out that the formula (14.1) is the approximate form of the first order. In fact, the exact formula is f = 1-v because “the remote time is received whit the period T’=t’2-t’1=T(1+v/(c-v))=T/(1-v/c).”

    This means that your thoughts about the values of v are not at all eligible for physics.
    In fact, if B moves away from A and its speed becomes v≥1, any communication between them ceases and both A and B will disappear from the view of the other as if swallowed by a black hole. In this case the exact form f = 1-v would give a negative frequency highlighting the absurdity of such a physical condition.

  88. claesjohnson

    No, in recession a velocity greater than the speed of light is possible, while still keeping contact.
    This is shown by galaxies seen far away seemingly receding with a velocity greater than the speed of light, with redshift z > 5.

  89. Michael

    In my common logic: If a bullet travels more slowly then the body that one wants to hit, the bullet never reaches the body. How can we measure the redshift of a galaxy if its emitted light isn’t able to reach us?

    • Claes Johnson

      It is like the sound from a supersonic jet airplane, which reaches you, right?

  90. Michael

    I think kinematics isn’t an opinion.

    In this case A sends radio pulses with a period T and B receives them with the period T ‘.
    At time t0 A sends the first pulse while B is in the position X0, so B receives that impulse at time t1 = t0 + X0 / (c-v).
    At time t0 + T, starts the second pulse when B is in the position X0 + vT and B will receive it at time t2 = t0 + T + (X0 + vT) / (c-v).
    So, B receives the pulses of A with the period T ‘ = t2-t1 = Tc / (c-v), i.e. with the frequency f’ = f (1-v / c) and vice versa.
    We can also use the form f’ = f / (1 + v/c – …. + ….) or T’ = T(1 + v/c – …. + ….) where “….” are terms of second order or more.
    Notice that the redshift is (λ’-λ)/λ = (T’-T)/T = 1/(1-v/c) and solely with v/c <5 seems very wrong.

    Also, nobody hears an arriving supersonic aircraft as its noise is present at subsonic velocity only inside the Mach cone at the back of the airplane and you can hear it only after that it has passed over your location.

  91. Michael

    Errata corrige.
    There is some issue with special characters.

    Notice that the redshift is (λ’-λ)/λ = (T’-T)/T = 1/(1-v/c) and solely with v/c much smaller than 1 you can say that the redshift is (λ’-λ)/λ = 1+v/c. Really, using the approximate form with z=v/c>5 seems very wrong.

  92. claesjohnson

    I said that you can hear a supersonic plane when receding, and you seem to agree, Fine.

  93. Michael

    Well, I must admit I was wrong and a lot too.

    There is no symmetry for the effect Doppler between emitter at rest (only case considered by me) and emitter in motion.
    I still have a doubt though. The symmetry certainly exists for the relative velocities and therefore we should have

    λ ‘/ λ = (1 + v/c) / (1 – v/c) and for a velocity v much smaller than c

    λ ‘/ λ = (1 + v/c)² = 1 – 2v/c as (v/c)² is certainly negligible.

    Right?

  94. Michael

    Errata corrige
    Of course
    λ ‘/ λ = (1 + v/c)² = 1 + 2v/c as (v/c)² is certainly negligible

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