I believe that a glaring problem in Physics education today is that instructors are too concerned with presenting mathematical formalisms divorced from any context of physical intuition. Much of modern Physics has become a branch of Applied Mathematics and, as such, should now fall under the tutelage of University Mathematics departments. Many Physics programs around the world might as well close down the Freshman laboratories and send everyone packing to the Mathematics building. There simply is not enough concentration on having students think intuitively or pragmatically in an attempt to understand physical phenomenon.

Even less priority is placed on giving students any rudimentary understanding of the origins of the theories they are presented with. Obviously, education in Physics must include a reliance on the theoretical tools which physicists employ. As such, a great majority of time must be devoted to mathematical formalism. However, too often, universities are churning out applied mathematicians, not scientists. They are not thinking like scientists. They are thinking like mathematicians. The fact that there are String Theorists stating that perhaps we should reevaluate what it means for a theory to be verified kind of gets to the heart of the problem. In many cases, it appears that some communities in Theoretical Physics are losing sight of the larger picture and have become too laden down in mathematical formalism. The actual Physics is nowhere to be seen.

This exclusive reliance on abstract mathematical formalism causes many to lose sight of the fact that Physics is an empirical science and always will be one. Most students of Physics will have one rudimentary freshman lab requirement and then perhaps a laboratory course in electronics. After that, they will never step foot inside of a laboratory for the rest of their professional lives.

IMO, Maxwell's, 'A Dynamical Theory of the Electromagnetic Field' should be required reading in E&M and portions of Newton's 'Principia' should be required in the obligatory Mechanics course.

What was the physical intuition Maxwell used? How about Newton? What was he really thinking and from where did the impetus for his ideas come? How did he arrive at what he did?

You would be surprised at how much your own understanding of the classic subjects is enhanced by thinking along with the original source(s) instead of relying exclusively on the highly generalized, modern version of the subject that is presented. Having an instructor throw out the equations and tell students to sit down and do the problem sets totally sterilizes the subject matter and turns our future scientists into automatons.

    James,

    Sorry about that. To be clear, I take the non-absolute nature of time to be an empirical result so, to me, it's not using relativity to support relativity. But I am of the opinion that we have to rely on empirical results to at least some extent because we built technology out of this stuff and it's all got to work and be consistent.

    Regarding your fundamental quantities, I might agree with space and time, but I definitely don't agree with force, at least how it is presently defined. I might be inclined to agree if we found a "broader" definition that took into account non-interaction-related correlations.

    As for things like black holes, even Newton predicted them. But my point is that the empirical evidence of their existence seems irrefutable. See, I personally believe that theory works best when it is based on empirical results since, for better or for worse, that's the window through which we view the world.

    Eckard, yes energy does relate to h-bar.

    Ian

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    • Post #83

    Marcel,

    I did not find an essay of you on the topic time, and I looked in vain into your essay on the topic"what is ultimately possible" for a more understandable to me explanation of your negative probability.

    As an engineer I am familiar with negative values of resistance (du/di, not u/i). I also know that the same distance can be attributed to a negative x coordinate as well as to a positive radius. In all, there are several cases where negative values are reasonable. Velocity can change direction. Nonetheless I maintain that basic physical quantities are scalar ones that have a natural reference zero and primarily no negative values.

    Could you please give a reference that might help me to understand your negative probability? If I understood you correctly, you consider a small box (part of space) that might or might not contain at least one a particle. Correct? Well you wrote probability of finding instead of probability of being in the box. However, you did not yet reveal to me your method and criterion of finding.

    Given you did consider as usual the particle(s) contained or found in any case if only it was in the box at least once within the given timespan. Then I did not doubt that you understood: Extending the timespan of observation can only increase the probability. Are you familiar with conditional probability?

    Given you did count the total time a single particle might be expected to be in summa located in the box on average, and the likelihood of being contained decreasing with time, then I could also imagine the average probability reduced or even equal to zero but never negative.

    Incidentally, do you share Cantor's opinion that there are more real numbers than rational numbers? Are there more positive and negative numbers altogether as compared to just the positive ones? I am challenging your forensic experience.

    Eckard

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    • Post #84

    Eckard,

    As usual, I need to ponder this. Hmmm. I'm not sure which statement you're talking about (which one I corrected). Can you remind me? And, without sounding like too much of an idiot, what's TND again?

    Ian

    I think only FQXi members can start threads here for whatever reason. If you want me to start one, give me some initial thing to start it with (a comment or something) and I will (as long as it's foundational I guess). It would probably be good only because it's becoming harder and harder to figure out what I've replied to and what I haven't on this thread since it's gotten so long!

    Amen to that. We try to give our students a broad background and, though I'm a theorist, I always make an attempt to make it "physical." In fact, Carl Caves once said essentially the same thing (we can't lose site of the physicality).

    You should really read Moore's Six Ideas That Shaped Physics. It really tries to teach what you're talking about - that conceptual under-current that is so crucial.

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    • Post #87

    Ian,

    Thanks for lecturing. My question concerning h was rather a rhetoric one, and I intended to express my opinion that h or h_bar is just a real coefficient comparable with my or epsilon. I do not consider the "quantum of action" and so called quantization condition something peculiar. On the contrary, in my eyes, the re is no essential difference between the relationships frequency/time and momentum/distance. Both are subject to the uncertainty relation which I did visualize in my essay 527 with restriction to R, i.e. without the imaginary unit!

    I should warn everybody: My approach demands to admit that future events cannot have any influence and therefore the very moment is the only reasonable absolute reference point t=0 of elapsed time. Admittedly hard to believe but mathematically correct as soon as some tiny and mostly overlooked flaws in the foundations of mathematics will be amended. Ask your self: Is it justified to deny the use of Dirac impulse at zero just because mathematicians without feeling imagined it symmetrical to zero?

    Eckard

    Eckard,

    I missed the contest on the nature of time and the essay on the limits of physics does not mention negative probability.

    .... "that have a natural reference zero"... If you think in absolute terms yes, but in relative terms, there may be a negative values..

    I re-read my post and it is not all too clear.. The idea of a negative probability came to me when looking for a wave-like distribution that would represent motion as for an associated wave. I made the graph of the function (gauss minus SIN). It gave a kind of a skewed distribution with a negative first half wave and an above normal for the second half, for a motion in the plus x - axis. This was what I was looking for as a distribution representing a wave made of a variation of the rate of passage of time. Just as the time rate gradient causes gravitational fall, the structure of this distribution represented inertia as a probability distribution based on a wave of variation in the rate of passage of time. ( to understand this passage of time you must go back to the essay that explains the logical origin of the substantial passage of time)

    Calling the first half of the (gauss - sin) graph a "negative probability" appeared natural to me because it was below the x axis. The second half of the graph is higher than the normal probability, which suggests a relative higher probability. One may understand the directionality and spontaneity of this pair by the conjunction of this negative probability and higher than normal probability...

    The original idea was that pushing a particle would change its gaussian normal probability to a skewed (gauss - sin) type of probability representing now its inertial motion. (this is an absolute metaphysical explanation, so, forget in this context the empirical Relativity point of view)

    I don't know about conditional probability and do not know about Cantor's opinion. But I am interesting in a natural origin to the structure of numbers i.e. even - odd - prime numbers. Can you tell me in short if and how this conditional probability could apply to the above exercise?

    Thanks,

    Marcel,

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      • Post #89

      Ian,

      I have to apologize for my distracting carping concerning "I guess I see". "I guess I always did see" is logically correct.

      TND stands for the Latin words tertium non datur and means either or, there is no third possibility in between. Brouwer claimed and already Galilei understood: This is valid for finite but not for infinite quantities. You are not at all an idiot but a Member.

      What about me, should I have reason to feel disappointed because virtually everybody hesitates supporting my reasoning? Not before someone presented at least one tangible counter-argument.

      Eckard

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      • Post #90

      Marcel,

      Given a salesman offers 50% off and an additional 40 % reduction. Does this mean you have to pay just 10%? Why do you feel entitled to simply add probabilities?

      You may add velocities but you have to multiply reductions of price as well as probabilities. Ergo, probability can neither get smaller than zero nor larger than one. You were muddling probability with velocity.

      What about the question whether or not the positive plus negative numbers together are more than only the positive ones, Cantor found it correctly out but he admitted to Dedekind: I cannot believe it. Take his doubt as an other example for a typical fallacy due to superficial thinking.

      Forget unnecessary musing about even, odd, and prime numbers. You should rather ask yourself why on cannot put zero and infinity in these drawers. The original structure of numbers, as already be found in Euclid's definitions, was carelessly abandoned in the 19th century mathematics.

      Eckard

      Eckard,

      "Given a salesman offers 50% off and an additional 40 % reduction. Does this mean you have to pay just 10%? Why do you feel entitled to simply add probabilities?"

      --- In dealing with the probability of position of a particle... the sum must be one; the particle exists somewhere. But, it is more of an image. Gravity is often portrayed as a dip in a sheet, an attractor for balls rolling in the vicinity. Consider now a bump in the same sheet. Place a ball on the bump and it will leave in whatever direction... this bump is my negative probability.

      "You may add velocities but you have to multiply reductions of price as well as probabilities. Ergo, probability can neither get smaller than zero nor larger than one. You were muddling probability with velocity."

      --- I know I am muddling something in my explanation, but it is not what you say.

      "What about the question whether or not the positive plus negative numbers together are more than only the positive ones, Cantor found it correctly out but he admitted to Dedekind: I cannot believe it. Take his doubt as an other example for a typical fallacy due to superficial thinking."

      --- Superficial reading: Since the early Greek philosophers, we have understood the distinction between two important concepts: the underlying reality and our perceptual experience. Over the centuries, we have always mixed the two concepts at the same time and amounted to nothing. Around the time of Newton, Descartes and others, the empirical method was born. We would forget for now/for now about the underlying reality and would consider the universe as a black box. We would concentrate our study on our experience of the black box, i.e. the empirical concept and approach and find the laws that best described our experiences. But no matter how successful the empirical concept is in this year 2010, the other concept (underlying reality) is still sitting on the back burner where we left it 300 years ago. Because we do not know what the universe is made of (what is the substance) and what makes it work by itself (the cause), all of our best science remains an educated guess on outcomes. And, that is the limit of physics. Your superficial reading of my essay did not reveal this to you. Unless one understands this state of affair, he cannot ask the question and the answer to this question certainly means nothing to him. The future of physics lies with metaphysics.

      "Forget unnecessary musing about even, odd, and prime numbers. You should rather ask yourself why on cannot put zero and infinity in these drawers. The original structure of numbers, as already be found in Euclid's definitions, was carelessly abandoned in the 19th century mathematics. "

      ----- My monistic description of the universe suggests that there is a natural and logical structure under the even odd and prime numbers... and maybe not... not loosing too much sleep over that one.

      Marcel,

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        • Post #92

        Spanner?..just where does infinity begin?..somewhere between 0 1?

        Infinity cannot possibly start from Zero, so it has to be One. The fractional reduction from 1 to 0 cannot produce the same "infinity" as the continueous whole number "infinity"? There can never be a total discrete zero, a very finite part "fraction" will exist for all Zero's.

        In the opposite continuum, there can never be a viable "total" infinity, a continuum of whole consecutive numbers. One can class the Prime number process, when a new number is reached infinity is falsefied, but as infinity is a function of "time", you will eventually come across a prime number that will take a certain time to discover, or check, tou will need the collective time of at least TWO Universe's!

        It is not where Infinity ends that is important, it is where one defines its source?

        Ian your succint discrete point_infinity does not equal your total continuous infinity by fact of functioning time constraints?

        Best p.v

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          • Post #93

          Hi Ian,

          Thank you for your reply.

          "...To be clear, I take the non-absolute nature of time to be an empirical result so, to me, it's not using relativity to support relativity. ..."

          I assumed that was the case. It is the answer adopted by theoretical physicsts. I am not one, however, this is the way I see it:

          Yes clocks will measure different intervals due to distance from mass. They are not intervals of time; they are intervals in time. Everything occurs durring time. This is not evidence that time controls everything. It is evidence that the cause of a particular activity is changing. Is time is a cause of activity and does time control the rate of activity? To prove either of those possibilities we need to perform experiments on time? Experiments on clock's of any type is no more informative that experiments on any other activity in the vicinity of the measurements. GPS adds only more additional information about how physical activity varies with respect to distance from mass. Unless time is established as the cause of all of this activity, then time is not the subject of the measurements.

          The time dilation equation is actually the t dilation equation. The t in physics equations is a measure in time (some duration of some physical activity) and not of time (as in a testable property in itself). All activity is measured with respect to a standard of activity. That standard can be chosen by virtue of its exhibiting as stable as practical cyclic activity. For example, if one wished to measure the rate of cyclic activity A, one would compare it to the standard for cyclic activity. Both of these cyclic activities are material in nature and are therefore subject to effects brought upon them by other material objects. In other words, they both are variable.

          We use the name seconds for the unit of measurement in physics equations: however, in the most fundamental sense, the units of t should be referred to as cycles of the standard chosen. So, by measuring cyclic activity A against the standard cyclic activity B, The true fundamental form of the units for both of them is (#cyclesA)/(cycleB). The property of time is not shown to be affected by this action. All activity requires time to occur. The time taken is a duration in time simply because time is passing during the activity. Time itself is not a physical property that can be sliced up, contained, or molded into a new form.

          "...But I am of the opinion that we have to rely on empirical results to at least some extent because we built technology out of this stuff and it's all got to work and be consistent. ..."

          I think it is crucial to remain dependent upon empirical results as closely as possible and to use theory only when necessary to risk moving forward in analyses in the face of the unknown. That is why I first refer back to photons as our source of information. They tell us that particles of matter changed their velocities. If there is no change of velocity, then we receive no information. There has never been an experiment that included a change of velocity for either time or space. They just are not available for us to trap and experiment upon.

          "...Regarding your fundamental quantities, I might agree with space and time, but I definitely don't agree with force, at least how it is presently defined. I might be inclined to agree if we found a "broader" definition that took into account non-interaction-related correlations. ..."

          I use the word force in a generic form, meaning that anything that causes change of velocity is a force. Gravity is a force. If a change in position of one object causes a change in position of another object, regardless of whether or not it is faster or slower than the speed of light, then I think that indicates a force exists. I see no fundamental problem with allowing for this possibility. I see it as analogous to saying that the speed of light is a constant in free space. Any coordinated behavior acrossed the universe is evidence that something is controlled by a means that exists outside the limitations of the speed of light.

          "...As for things like black holes, even Newton predicted them. But my point is that the empirical evidence of their existence seems irrefutable. See, I personally believe that theory works best when it is based on empirical results since, for better or for worse, that's the window through which we view the world. ..."

          Newton's black hole and Eistein's black hole are very different. Einstein's relies upon the existence of spacetime. There is no evidence that either space or time are affected by the activities of matter. There is evidence that matter affects other matter and that matter and light both affect each other.

          I guess this might be getting tedious for you. I appreciate your time. I will let you have the last word. You are the expert.

          James

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          • Post #94

          Marcel,

          You wrote: "In dealing with the probability of position of a particle... the sum must be one; the particle exists somewhere. ... Gravity is often portrayed as a dip in a sheet, an attractor for balls rolling in the vicinity. ... Place a ball on the bump and it will leave in whatever direction... this bump is my negative probability."

          -- I understand dip and bump as attractive or repulsive force, respectively, which are factors that influence an otherwise random motion. Addition is only allowed as a linear approximation for small values.

          I am not familiar with monism. I merely know that it relates to Ostwald, Haeckel, Parmenides, and Zeno. My old dictionary calls it a naive kind of materialism. Admittedly, I did not yet read your essay at all. I just used the search option for negative probability as to clarify whether there is any reasonable use of negative probability.

          Yes, around 1650, the time between Descartes (1596-1650) and Newton (1642-1727), Guericke contributed to the experimental method. His intention was to understand the forces that rule the motion of planets, and eventually this gave rise to steam engine and electricity. Guericke did not like mere speculation. You wrote: "The universe as a black box". Did you not understand that we are living within this box and have no possibility to look at it from outside? The very notion universe is in this sense a prison we cannot escape. This is however no relevant limit to physics if we accept that within the notion universe there is enough to investigate. It is perhaps possible to find almost any causes of something tangible but definitely impossible and therefore useless to deal with "the" primary cause. Causality and time are nearly synonymous in that they structure all events that already happened (probability one), to be seen from the chosen point of view (probability of correct observation smaller than one). Future causality and future time are not yet observable and more or less uncertain. Do you object?

          Eckard

          Eckard,

          What I understand is that we dropped the ball some 300 years ago and I picked it up. My essay is my answer to the best of my abilities. So, it is possible/possible to ask and answer the question. What I need are people who can wrap their mind around this concept and back engineer it into our present knowledge to make it complete.

          (Complete knowledge = physical description logical understanding.)

          "..mere speculation.... have no possibility... of something tangible... definitely impossible and therefore useless.."

          These words tell me that you are not one of those people. (Maybe I'm not in the right forum ..)

          All the bests,

          Thanks,

          Marcel,

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            • Post #96

            Marcel,

            Yesterday LHC has been switched on again. I will appreciate a negative outcome that could possibly give rise for taking R more seriously and use mathematics no longer without knowing what is really behind it.

            I will quote you because you are still considering yourself a monist:

            "Understanding is about knowing the logic behind the existence and evolution of the universe."

            --- Logic behind the existence of the universe? As it is meant, this sounds unrealistic to me, because I understand the universe as something unlimited and ergo comprehensive but incomprehensible.

            I rather see the logic behind the existence of the notion universe.

            "The metaphysical and logical understanding of the universe is accessible, understandable and necessary for us to progress beyond the limits of physics. It is certain that this metaphysics still has to be engineered back into physics in order to produce something new and practical in our reality.

            --- Understandable understanding. Hm.

            "The universe has existed and evolved by itself for about 14 billion years."

            --- Isn't this a hypothesis that is based on results from the experimental method?

            --- Doesn't it contradict to Monist Parmenides: "The universe consists of only one object, it exists timelessly and changelessly." "There is no motion, since motion implies the existence of more than one thing, namely, a finishing place and a starting place."

            Zeno tried to demonstrate something I do not deny: "True existence evades measurement."

            --- No further comment,

            all the best for you and respect for your effort,

            Eckard

            Let's have you Marcel LeBel the last word: The box contains everything physicists ever wanted to know about the universe. The content of the box is the only thing that will allow us to make sense of all the theories and equations (unification). But they can't get it with the empirical approach. The empirical approach is about finding things by experience, trial and error. It is a choice we made long ago between knowing and doing. The empirical test is not just the proof of a theory. It is before all a practical demonstration of control over some segment of the universe and this control provides the illusion that we understand what we are doing. We don't

            James,

            Thanks for the clarification on those points. I think you might have some interesting points to make, though I'm not sure I agree with them all (that, of course, does not mean they are wrong, simply that I have a different view).

            I think your reliance on photons is interesting since the one thing that does not change regardless of how we look at it, is the speed of light being a maximum no matter what units we measure it in or what frame we look at it in. I also like your idea of "cycles" as a measure of time, though I should note that, for awhile, that was actually how the international standard of a "second" was obtained (it was based on some number of cycles of something to do with cesium, if I recall - it's been awhile).

            I absolutely think there's a problem with the existing definition of "force" and your more general definition might be a good starting place for fixing it.

            And this is definitely not tedious. Rather, it is enjoyable. Unfortunately I got busy the last couple of days and couldn't check up on this until just now.

            Cheers,

            Ian

            Eckard,

            Ah! OK, I see. (I'm still pondering...)

            Ian

            Paul,

            "Ian your succint discrete point_infinity does not equal your total continuous infinity by fact of functioning time constraints?"

            I'm not sure I follow you here. Can you clarify?

            Ian

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            • Post #100

            Paul,

            So called Rhind Papyrus shows how the old Egyptians in 1650 B.C. calculated with fractions. When Thales (624-545) stated that everything is made of water, he meant the physical universe should not be understood in terms of unconnected fragments but in terms of something continuous. His compatriot Anaximander (610-540) imagined infinitely many worlds, all made out of something infinitely extensed that has always existed ans will always exist. Pythagoras (570-500) claimed the opposite: All is number. This was proven wrong by irrational numbers. Parmenides (480) evaded infinity by rejecting it which in connection with assumed continuity led to the paradoxes of Zeno (450)

            Aristotele (384-322) pointed out that infinity is the possibility to count endlessly. He was definitely correct in that there is no largest number infinity: Infinity actu non datur (There is no actual infinity).

            Let me skip the further history and ask how for instance Dirichlet and Dedekind were misled by the obvious fact that infinite Fourier series must be complete. They concluded that "infinity" must be reached. Constructivists like Kronecker and Brouwer objected that infinity cannot be reached within finite time. This might be behind your "time constraints".

            I do not share this point of view, and mainstream mathematics did also reject this idea of becoming.

            My suggestion is slightly different. Well, we may operate with the fictions of the infinitely small as well as the infinitely large. We just have to avoid the mistake to believe that they can be reached by splitting or adding, respectively. They are no quantities but describe ideal qualities. In contrast to the mandatory tenet, infinity is not exhaustible.

            Are numbers infinitely exact? This is an indispensable assumption. However, I maintain that we have to distinguish between rational and real numbers. While the sequence of natural numbers is changed if we add or remove a singular number we must not infer that for instance exclusion of pi from the continuum of the real numbers has any effect on this continuum. It simply does not matter because the distance between pi and the "next" larger number has the measure zero. That is, as some most excellent mathematicians understood: The TND is invalid in this case. Brutal mathematicians tried to remove the difference between 0.999... and one in Hilbert's manner by means of definition. Why not admitting that continuum and discrete numbers are mutually complementing but also mutually excluding qualities? This would not harm reasonable mathematics but show where Dirichlet and Dedekind went wrong.

            Eckard