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Thread: Why is acceleration inversely proportional to the mass?

  1. #1 Why is acceleration inversely proportional to the mass? 
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    Hello everyone,

    I was wondering, is the acceleration only inversely proportional to the mass or to the rest energy of a body?

    An electron for instance gets its rest energy from interacting with the Higgs field ( by absorbing ziggs particles if I get it right). A given amount of energy will accelerate the electron inversely to its mass.

    However, if the speed of light was different, the rest energy of the electron mc^2 would be different. So would the acceleration still be the same?

    In other words, is the acceleration inversely proportional to the mass or the rest energy?


    In the case of a proton, most of its energy does not come from the interaction of the quarks with the ziggs (the individual masses of the quarks), but from the energy of interaction between the quarks. What we usually call the mass of the proton is in fact rather its rest energy. And the acceleration that the proton is subjected to does not depend only to its 'higgs' mass ( given only by the interaction with the higgs field).

    In other words, does F=ma describe the phenomenon of acceleration accurately? Or in fact is it more the rest energy that is involved than just m?

    Nick.


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    F = m.a refers to the rest mass. But, as you say, some of that mass comes from the energy of the object.


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    Quote Originally Posted by Strange View Post
    F = m.a refers to the rest mass. But, as you say, some of that mass comes from the energy of the object.
    Hi Strange. So to get the mass you devide the rest energy of the object by c^2? In other words, the speed of light has no effect on the acceleration. If the speed of light was say 10 times higher, a certain force would still accelerate the object by the same amount ( not considering relativistic speeds).
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    Quote Originally Posted by Nic321 View Post
    Hi Strange. So to get the mass you devide the rest energy of the object by c^2?
    If you know the energy, then I suppose that is true. However, in general, all you know is the mass. It makes no practical difference whether you consider that mass to arise from binding energy, the Higgs mechanism or some other cause.

    The rest energy is simply the rest mass multiplied by c2.

    In other words, the speed of light has no effect on the acceleration. If the speed of light was say 10 times higher, a certain force would still accelerate the object by the same amount ( not considering relativistic speeds).
    These kinds of counter-factual questions are hard to answer. At the simplest level, if the speed of light were different then the binding energy in a proton, for example, would contribute a different amount to the rest mass. However, if the speed of light were different, then I suspect protons would not exist, unless you changed a lot of other fundamental constants to match. In which case, who knows what the answer would be...

    But someone with more knowledge might be able to give a better answer.
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    Quote Originally Posted by Strange View Post
    But someone with more knowledge might be able to give a better answer.
    Most fundamental constants are interrelated; for example, the gravitational coupling constant is inversely proportional to the speed of light, even though it is dimensionless. If you change just one fundamental constant without adjusting all others, you will "break" the laws of physics in the process. It turns out that the universe is an incredibly fine-tuned, yet very stable construct; why that is so, we don't really know for sure.
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Nic321 View Post
    Hi Strange. So to get the mass you devide the rest energy of the object by c^2?
    If you know the energy, then I suppose that is true. However, in general, all you know is the mass. It makes no practical difference whether you consider that mass to arise from binding energy, the Higgs mechanism or some other cause.

    The rest energy is simply the rest mass multiplied by c2.
    Ok, I see what you mean. I was thinking about that because I was wondering about why the speed of light and of the mass are invariant. I was wondering whether it could be related to the fact that F=m.a., and that E=mc^2. I don't know...

    Would you happen to know if there an explanation for why F=ma?


    These kinds of counter-factual questions are hard to answer. At the simplest level, if the speed of light were different then the binding energy in a proton, for example, would contribute a different amount to the rest mass. However, if the speed of light were different, then I suspect protons would not exist, unless you changed a lot of other fundamental constants to match. In which case, who knows what the answer would be...

    But someone with more knowledge might be able to give a better answer.
    Ok. It is hard to speculate what would happen if the constants where different, but I am under the impression that F=m.a is a very general equation and it is probably true in any universe similar to ours( if such universe exist!). However, Like you and Markus say, the force might well depend on the constants.

    It is the same for the invariance of the speed of light or the invariance of the mass, I would speculate it is probably true in every universe similar to ours.

    That is pure conjecture you might say.
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    Hi Markus. I checked the wikipedia page about the gravitational coupling constant:
    Gravitational coupling constant - Wikipedia, the free encyclopedia

    It says that alpha g = (Gme^2)/(hbar.c) = (me/mp)^2.

    That would mean that mp=sqrt (hbar.c/G).

    I find it surprising that the mass of the proton depends only on hbar, c and G. Is that correct?


    Apart from this, I was wondering some time ago about whether the gravitational constant G could depend on c or on other constants. Would that be possible?

    Nick.
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    Quote Originally Posted by Nic321 View Post
    Would you happen to know if there an explanation for why F=ma?
    As far as I know, it is just an experimental observation. I don't know if there is a deeper explanation. Probably not, as I think it is only a non-relativistic (Newtonian) approximation.
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    Quote Originally Posted by Nic321 View Post
    I find it surprising that the mass of the proton depends only on hbar, c and G. Is that correct?
    That's not the mass of the proton, it's the Planck mass.

    Would that be possible?
    Yes, one can express G in terms of planck mass, planck length and planck time, all of which in turn are defined via yet other fundamental constants...you get the picture. Everything is interconnected in modern physics.
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Nic321 View Post
    Would you happen to know if there an explanation for why F=ma?
    As far as I know, it is just an experimental observation. I don't know if there is a deeper explanation. Probably not, as I think it is only a non-relativistic (Newtonian) approximation.
    If you take the Coulomb force for instance, you still have F=ma = 1/4pi epsilon0 q1q2/d^2.

    Whatever the force the acceleration is always inversely proportional to the mass.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Nic321 View Post
    I find it surprising that the mass of the proton depends only on hbar, c and G. Is that correct?
    That's not the mass of the proton, it's the Planck mass.
    Oups, sorry about that, I didn'd see it was the Planck mass.

    Would that be possible?
    Yes, one can express G in terms of planck mass, planck length and planck time, all of which in turn are defined via yet other fundamental constants...you get the picture. Everything is interconnected in modern physics.
    Ok maybe G depends on c, I guess it's hard to tell which constant is more fondamental than which one.


    However, one thing puzzles me about the Einstein's equation. There is a term in G/c^4 in front of the E-M tensor. Inside the tensor are the terms mc^2 I believe. So it would mean that the curvature depends on mc^2/c^4, that is m/c^2.

    In other words, the curvature of space around a mass would depend on m/c^2. The larger c is the lower the curvature.

    Does that mean that there is an inverse relationship between gravity and the speed of light?

    I am under the impression that I probably got it wrong...
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    Quote Originally Posted by Nic321 View Post
    Hi Markus. I checked the wikipedia page about the gravitational coupling constant:
    Gravitational coupling constant - Wikipedia, the free encyclopedia

    It says that alpha g = (Gme^2)/(hbar.c) = (me/mp)^2.

    That would mean that mp=sqrt (hbar.c/G).

    I find it surprising that the mass of the proton depends only on hbar, c and G. Is that correct?


    Apart from this, I was wondering some time ago about whether the gravitational constant G could depend on c or on other constants. Would that be possible?

    Nick.

    It's not that it predicts just a ratio, it's a number which pops up everywhere in physics. It can define the ratio of different field strengths, is the gravitational fine structure, which happens to be the ratio (electron mass over the Planck mass squared). The electromagnetic fine structure is .
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    Quote Originally Posted by Nic321 View Post
    Does that mean that there is an inverse relationship between gravity and the speed of light?
    The Einstein constant is just a proportionality factor between the energy-momentum tensor and the Einstein tensor; it is fixed by the boundary condition that these equations must reduce to standard Newtonian gravity in the weak field limit, i.e. to the classical Poisson equation. The rest is simply down to a choice of units. It also needs to be remembered that these equations aren't solved for the components of the Einstein tensor, but rather for the metric - which makes them coupled and highly non-linear, so there is no direct proportionality relationship. Having said that, the value of the speed of light does of course play a role here - change it, and you change the equations.
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    Quote Originally Posted by Nic321 View Post
    Hi Markus. I checked the wikipedia page about the gravitational coupling constant:
    Gravitational coupling constant - Wikipedia, the free encyclopedia

    It says that alpha g = (Gme^2)/(hbar.c) = (me/mp)^2.

    That would mean that mp=sqrt (hbar.c/G).

    I find it surprising that the mass of the proton depends only on hbar, c and G. Is that correct?


    Apart from this, I was wondering some time ago about whether the gravitational constant G could depend on c or on other constants. Would that be possible?

    Nick.
    Like all important fundamental dynamical processes in nature, physics often described them in terms of the constants of nature, such as the speed of light, permittivity, permeability, the gravitational constant ect. The CODATA elementary charge does exactly this. The most accurate value of the elementary charge is





    Even from this you can derive accurate values of that features in the fine structure





    You can derive, just as Markus said, anything from the fundamental constants of nature. They are like the ''ingredients'' of god.
    Last edited by Chesslonesome; May 9th, 2014 at 09:28 AM.
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    Quote Originally Posted by Chesslonesome View Post
    Like all important fundamental dynamical processes in nature, physics often described them in terms of the constants of nature, such as the speed of light, permittivity, permeability, the gravitational constant ect. The CODATA elementary charge does exactly this. The most accurate value of the elementary charge is




    Nope, it isn't, the correct value is or
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    I see Chesslonesome, but I am under the impression ( maybe I am wrong ) that with these fine structure constants you always reuse the same constants that have been defined in a certain way. It's like when in math you reuse the same equations and you do substitutions, you always get back to the initial equation more or less.

    It is amazing that the universe has so few constants. I once heard a scientist say there were 8 fundamental constants, the others being derived.


    As for why the fundamental constants have the value they have, if we are in an inflationary universe ( which could be true given the confirmation of inflation last month ), maybe their values are set during the inflation. The era of normal expansion ( after the inflation) is maybe much more "calm", so it's less likely to produce changes in those constants. I would be curious to know what the scientists who work on inflation would speculate on that.


    Btw I search a bit on the gravitationnal coupling constant, you may be interested in this:
    vixra.freeforums.org - View topic - Gravitational coupling constant and fine structure constant

    The guy has maybe found a relation between coupling constants, I am not sure how relevant it is.
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    Quote Originally Posted by Nic321 View Post
    I see Chesslonesome, but I am under the impression ( maybe I am wrong ) that with these fine structure constants you always reuse the same constants that have been defined in a certain way. It's like when in math you reuse the same equations and you do substitutions, you always get back to the initial equation more or less.

    It is amazing that the universe has so few constants. I once heard a scientist say there were 8 fundamental constants, the others being derived.


    As for why the fundamental constants have the value they have, if we are in an inflationary universe ( which could be true given the confirmation of inflation last month ), maybe their values are set during the inflation. The era of normal expansion ( after the inflation) is maybe much more "calm", so it's less likely to produce changes in those constants. I would be curious to know what the scientists who work on inflation would speculate on that.


    Btw I search a bit on the gravitationnal coupling constant, you may be interested in this:
    vixra.freeforums.org - View topic - Gravitational coupling constant and fine structure constant

    The guy has maybe found a relation between coupling constants, I am not sure how relevant it is.
    "vixra" is a crank website and so is the author of the "paper" you are citing. Please stop.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Nic321 View Post
    Does that mean that there is an inverse relationship between gravity and the speed of light?
    The Einstein constant is just a proportionality factor between the energy-momentum tensor and the Einstein tensor; it is fixed by the boundary condition that these equations must reduce to standard Newtonian gravity in the weak field limit, i.e. to the classical Poisson equation. The rest is simply down to a choice of units. It also needs to be remembered that these equations aren't solved for the components of the Einstein tensor, but rather for the metric - which makes them coupled and highly non-linear, so there is no direct proportionality relationship. Having said that, the value of the speed of light does of course play a role here - change it, and you change the equations.
    So if I get you right Markus, the speed of light plays no role in weak gravitationnal fields. And that's why the speed of light doesn't appear in the newtonian equation. Is that correct?

    Also, would you say, generally speaking, that if c increases ( let's say the other constants are not affected), that the gravitational effect increases or decreases? That's a question I have wondered for quite some time. I had asked the question on a scientific forum a couple years ago but couldn't get a definite answer. It is hard to find someone who knows GR in enough detail to answer that kind of question.

    Thank you,
    Nick.
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    Quote Originally Posted by Nic321 View Post
    I see Chesslonesome, but I am under the impression ( maybe I am wrong ) that with these fine structure constants you always reuse the same constants that have been defined in a certain way. It's like when in math you reuse the same equations and you do substitutions, you always get back to the initial equation more or less.

    It is amazing that the universe has so few constants.


    Yes... in the mathematical sense, everything is related fundamentally-speaking, when you speak about universes and fine-tuned constants.

    It is when you try and build a system out of things which while fundamental are totally mysterious. Like the fine structure constant, there are many dimensionless figures in physics which hold physical meaning. At the heart of it, only dimensionless numbers are really real.

    There is a line of unification called G-h-c physics. It's an ''idea'' that maybe reality can be reduced to only these constants. The idea in itself is probably right, but there is probably more to reality than just these constants even though fundamentally-speaking all three constants unify in some way.
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    Quote Originally Posted by Nic321 View Post
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Nic321 View Post
    Does that mean that there is an inverse relationship between gravity and the speed of light?
    The Einstein constant is just a proportionality factor between the energy-momentum tensor and the Einstein tensor; it is fixed by the boundary condition that these equations must reduce to standard Newtonian gravity in the weak field limit, i.e. to the classical Poisson equation. The rest is simply down to a choice of units. It also needs to be remembered that these equations aren't solved for the components of the Einstein tensor, but rather for the metric - which makes them coupled and highly non-linear, so there is no direct proportionality relationship. Having said that, the value of the speed of light does of course play a role here - change it, and you change the equations.
    So if I get you right Markus, the speed of light plays no role in weak gravitationnal fields.


    The speed of light depends on two electromagnetic constants of the vacuum. Change any one of these constants, you change the speed of light.

    Barrow did some work on this.
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    Quote Originally Posted by Chesslonesome View Post
    The speed of light depends on two electromagnetic constants of the vacuum. Change any one of these constants, you change the speed of light.
    I think too many people place too great a significance, and indeed the wrong significance, on the formula:



    Firstly, has a chosen numerical value, and therefore isn't a property of reality. Secondly, the ampere is defined in terms of the force between two current-carrying wires, so is also not a measured value. Thirdly, the above expression is a combination of an electric and a magnetic constant, and because the magnetic field is relativistically connected to the electric field, it shouldn't be surprising that emerges from this. Furthermore, dimensional considerations indicate that in the above expression, all aspects of electromagnetism cancel, leaving only a speed.
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    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by Markus Hanke View Post
    Most fundamental constants are interrelated
    , , and are independent.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by Nic321 View Post
    As for why the fundamental constants have the value they have, ...
    To me, asking why the fundamental constants have the values they have is like asking why a metre is this (gesturing one metre) long. However, the values of dimensionless physical constants do require explanation. It is my personal view that these will be determined by a complete theory of reality, and that reality is not fine-tuned.
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    Quote Originally Posted by Nic321 View Post
    Also, would you say, generally speaking, that if c increases ( let's say the other constants are not affected), that the gravitational effect increases or decreases?
    There isn't a general answer to this, because "gravitational" effect in the context of GR would be geodesic deviation - and both the field equations as well as the geodesic deviation equation are differential equations, so the answer to the above depends on the specific scenario ( boundary conditions ) at hand.

    I had asked the question on a scientific forum a couple years ago but couldn't get a definite answer.
    That's because no definite answer exists. The Einstein equations are non-linear, so the effect of a change in constants will depend on what ansatz you use for the metric.

    So if I get you right Markus, the speed of light plays no role in weak gravitationnal fields.
    That depends what model you use. If you use Newtonian gravity, then the speed of light does not appear in the maths. If you use Einstein's GR, then c does appear in the equation. It is a question of the model you are using rather than of the physics.
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    Quote Originally Posted by KJW View Post
    , , and are independent.
    True - hence the qualifier "most"
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    Quote Originally Posted by Chesslonesome View Post
    Quote Originally Posted by Nic321 View Post
    I see Chesslonesome, but I am under the impression ( maybe I am wrong ) that with these fine structure constants you always reuse the same constants that have been defined in a certain way. It's like when in math you reuse the same equations and you do substitutions, you always get back to the initial equation more or less.

    It is amazing that the universe has so few constants.


    Yes... in the mathematical sense, everything is related fundamentally-speaking, when you speak about universes and fine-tuned constants.

    It is when you try and build a system out of things which while fundamental are totally mysterious. Like the fine structure constant, there are many dimensionless figures in physics which hold physical meaning. At the heart of it, only dimensionless numbers are really real.

    There is a line of unification called G-h-c physics. It's an ''idea'' that maybe reality can be reduced to only these constants. The idea in itself is probably right, but there is probably more to reality than just these constants even though fundamentally-speaking all three constants unify in some way.
    Ok so what you are saying is that from one universe to another, the physical constants (G, h, c, ...) may change, but there is a combination of those constants that will always give the same dimensionless number, and that this number has a special significance.

    What that means is that these constants are all intertwined. You can't change one without affecting the others, there's like a retroaction between them or whatever.

    That may be correct and it is an interesting idea, but it seems to me that what it tells us is how these constants interact with each other.

    I don't know but it seems logical to think that if something can change, it is made by a complex structure which can change, or is some sort of emergent phenomenon of something deeper. Which doesn't mean there couldn't be retroactions between them.
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    Quote Originally Posted by KJW View Post
    Quote Originally Posted by Nic321 View Post
    As for why the fundamental constants have the value they have, ...
    To me, asking why the fundamental constants have the values they have is like asking why a metre is this (gesturing one metre) long. However, the values of dimensionless physical constants do require explanation. It is my personal view that these will be determined by a complete theory of reality, and that reality is not fine-tuned.
    Ok, but there has to be a deep reason why the constants keep their values across time and space. Understanding why these constants keep their values would tell a lot on how the universe works, how space time emerges etc...

    I wonder, doesn't the fact that a constant remains identical hide a conservation law or something, some action reaction effect between the fields or whatever I don't know.
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    Quote Originally Posted by Nic321 View Post
    Ok, but there has to be a deep reason why the constants keep their values across time and space.
    Perhaps one could consider the universe as we see it to be a specific quantum state of an underlying system of degrees of freedom; then the fundamental constants would just be the free parameters that characterise the specific state. Just think quantum mechanics, but on cosmological scales...
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Nic321 View Post
    Also, would you say, generally speaking, that if c increases ( let's say the other constants are not affected), that the gravitational effect increases or decreases?
    There isn't a general answer to this, because "gravitational" effect in the context of GR would be geodesic deviation - and both the field equations as well as the geodesic deviation equation are differential equations, so the answer to the above depends on the specific scenario ( boundary conditions ) at hand.

    I had asked the question on a scientific forum a couple years ago but couldn't get a definite answer.
    That's because no definite answer exists. The Einstein equations are non-linear, so the effect of a change in constants will depend on what ansatz you use for the metric.

    So if I get you right Markus, the speed of light plays no role in weak gravitationnal fields.
    That depends what model you use. If you use Newtonian gravity, then the speed of light does not appear in the maths. If you use Einstein's GR, then c does appear in the equation. It is a question of the model you are using rather than of the physics.
    Thank you for the explanation.

    Newtonian gravity models gravitation in terms of a force, not in terms of space curvature. That may also be a reason why c doesn't need to appear.

    My question originally on the other forum was, would the moon crash on the Earth if the speed of light was to suddenly be increased by a factor of say 10. The energies mc^2 of both the Earth and the moon would immediately be increased by a factor of 100, the attraction would be much stronger and the moon would crash.

    From what I understand now, it wouldn't crash because the c^2 doesn't have an effect out in this scenario ( because of the weak gravitationnal field ).

    In other cases where the gravitationnal field would be much stronger, or in different scenarios it could be different, as you explain. In the case of 2 black holes getting close to each other for instance, from what I understand, there would be strong non-linear effect due in part to the speed of light.
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    Quote Originally Posted by Nic321 View Post
    Ok, but there has to be a deep reason why the constants keep their values across time and space.
    And why they have the values, they do, etc.

    On the other hand, we don't know for certain that they are constant. For example: Fine-structure constant - Wikipedia, the free encyclopedia: Is the fine-structure constant actually constant?
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Nic321 View Post
    Ok, but there has to be a deep reason why the constants keep their values across time and space.
    Perhaps one could consider the universe as we see it to be a specific quantum state of an underlying system of degrees of freedom; then the fundamental constants would just be the free parameters that characterise the specific state. Just think quantum mechanics, but on cosmological scales...
    By that do you mean that when a new universe pops up ( don't know how... ), the setting of the constants G, h, and c, you be probabilistic, in the sense that there would be no "heritage" from another universe or pre-existing another space-time?
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    Quote Originally Posted by Nic321 View Post
    Newtonian gravity models gravitation in terms of a force, not in terms of space curvature. That may also be a reason why c doesn't need to appear.
    Yes, that's right.

    My question originally on the other forum was, would the moon crash on the Earth if the speed of light was to suddenly be increased by a factor of say 10.
    This sounds like a deceptively simple question, but is actually very difficult to answer scientifically. The problem is that the masses of the moon and the earth are of a similar order of magnitude, so this is really a full general relativistic 2-body problem. This type of problem cannot be treated analytically, only through numerical methods. The only way to answer this question definitively would thus be to run the numbers ( with amended numerical value for c ) through appropriate software, and see what happens.

    The energies mc^2 of both the Earth and the moon would immediately be increased by a factor of 100, the attraction would be much stronger and the moon would crash.
    This is too simplistic a point of view. Like I said, you won't know what actually happens until you run the numbers for the GR 2-body problem, which is not a trivial undertaking.

    By that do you mean that when a new universe pops up ( don't know how... ), the setting of the constants G, h, and c, you be probabilistic, in the sense that there would be no "heritage" from another universe or pre-existing another space-time?
    Yes, pretty much. A similar point of view ( description of the universe as a wave functional, analogous to quantum mechanics ) is being put forward by the Wheeler-deWitt equation of quantum cosmology :

    Wheeler
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Nic321 View Post
    Ok, but there has to be a deep reason why the constants keep their values across time and space.
    And why they have the values, they do, etc.

    On the other hand, we don't know for certain that they are constant. For example: Fine-structure constant - Wikipedia, the free encyclopedia: Is the fine-structure constant actually constant?
    We probably have to live in a universe where the constants remains almost exactly the same, otherwise all the structures would desintegrate, so we wouldn't be here. But maybe a small margin of change is allowed.

    Maybe also most universes have constants that change much more than in ours, we just couldn't live in these ones.

    In any case, there has to be a mecanism that change those constants over time, in the very long term ( like in an inflationary universe). I have trouble buying the idea that the universe would necessarily have certain exact constants values that would suit our existence. There has to be some degree of evolution of the constants to explore all the possible values. So this means there has to be a mechanism that make these constants change, the equivalent say of cosmic rays for the DNA. Maybe that would be high temperature or whatever where quantum gravity comes into play.

    I like this video of Leonard Susskind where he describes the universe as a sort of creature with a DNA:
    https://www.youtube.com/watch?v=AzfhtouRM6s

    I am not sure I believe in string theory ( I am not competent to have an opinion on that ), but at least the idea of universes with changing physical constants equivalent of a sort of DNA makes sense to me to explain why finally a universe with the right constants for the emergence of intelligence life appeared.
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    Quote Originally Posted by Nic321 View Post
    Hello everyone,

    I was wondering, is the acceleration only inversely proportional to the mass or to the rest energy of a body?
    The short answer : IT ISN'T.
    The proof is simple:



    where


    As you can see, the acceleration is NOT inversely proportional to the mass because it is pretty clear that , in general, . Only for , .

    The fact that
    is pretty evident in particle accelerators, highly complicating the equations of motion.
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    This sounds like a deceptively simple question, but is actually very difficult to answer scientifically. The problem is that the masses of the moon and the earth are of a similar order of magnitude, so this is really a full general relativistic 2-body problem. This type of problem cannot be treated analytically, only through numerical methods. The only way to answer this question definitively would thus be to run the numbers ( with amended numerical value for c ) through appropriate software, and see what happens.
    Ok, the example of 2 bodies with masses in the same order of magnitude is very complicated, but what about let's say just the Earth and a satellite? Say you suddenly increase c by a factor of 10, what would happen? The mc^2 of the Earth is multiplied by 100, does the satellite crash in 30 seconds? I don't think so but I don't know...

    Would the result using general relativity still be consistant with newtonian gravity, which would see no difference because there is no c in the newtonian equation.

    I guess all this boils down to how the c gets cancelled from the general relativity equation in weak gravitational field, but I am not sure.

    Yes, pretty much. A similar point of view ( description of the universe as a wave functional, analogous to quantum mechanics ) is being put forward by the Wheeler-deWitt equation of quantum cosmology :

    Wheeler
    The link is really too complicated for me, but I get the idea that basically they are trying to quantize gravity.

    In your idea, would the constants G, h, c be quantized? Like they would have descrete values? Would they be correlated, in the sense that you change one, the others get modified?
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    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by Nic321 View Post
    Hello everyone,

    I was wondering, is the acceleration only inversely proportional to the mass or to the rest energy of a body?
    The short answer : IT ISN'T.
    The proof is simple:



    where


    As you can see, the acceleration is NOT inversely proportional to the mass because it is pretty clear that , in general, . Only for , .

    The fact that
    is pretty evident in particle accelerators, highly complicating the equations of motion.
    That's not what I was talking about but anyways.
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    Quote Originally Posted by Nic321 View Post
    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by Nic321 View Post
    Hello everyone,

    I was wondering, is the acceleration only inversely proportional to the mass or to the rest energy of a body?
    The short answer : IT ISN'T.
    The proof is simple:



    where


    As you can see, the acceleration is NOT inversely proportional to the mass because it is pretty clear that , in general, . Only for , .

    The fact that
    is pretty evident in particle accelerators, highly complicating the equations of motion.
    That's not what I was talking about but anyways.
    What you were talking about is WRONG, your question in the OP is ill-posed. The above proves it. You are trying to tackle complicated subjects but you obviously do not understand the basics.
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    Well... no.
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    Quote Originally Posted by Nic321 View Post
    but what about let's say just the Earth and a satellite?
    If we let the orbit entirely coincide with the equatorial plane, it is then a solution to the differential equation



    with the effective potential given by



    E is an integration constant that is fixed by boundary conditions ( it signifies energy per unit mass, which is a constant of motion ). As you can see, the speed of light explicitly shows up in the effective potential, so it will be part of the solution as well. This isn't an easy equation to solve; the analytic solution involves elliptic functions, and a bit of algebraic "creativity" as well. Here is how it is done in detail :

    Schwarzschild geodesics - Wikipedia, the free encyclopedia

    I am at work at the moment and don't have any way to plot the elliptic function, but from what I remember off-hand it seems that if you increase the speed of light, the orbital radius would increase as well, all other things being equal. I might be wrong though, and it depends on the boundary conditions as well. If I have time tonight I might plot it using Maple, and see what happens.
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    Quote Originally Posted by Markus Hanke View Post

    I am at work at the moment and don't have any way to plot the elliptic function, but from what I remember off-hand it seems that if you increase the speed of light, the orbital radius would increase as well, all other things being equal. I might be wrong though, and it depends on the boundary conditions as well. If I have time tonight I might plot it using Maple, and see what happens.
    See here.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Nic321 View Post
    but what about let's say just the Earth and a satellite?
    If we let the orbit entirely coincide with the equatorial plane, it is then a solution to the differential equation



    with the effective potential given by



    E is an integration constant that is fixed by boundary conditions ( it signifies energy per unit mass, which is a constant of motion ). As you can see, the speed of light explicitly shows up in the effective potential, so it will be part of the solution as well. This isn't an easy equation to solve; the analytic solution involves elliptic functions, and a bit of algebraic "creativity" as well. Here is how it is done in detail :

    Schwarzschild geodesics - Wikipedia, the free encyclopedia

    I am at work at the moment and don't have any way to plot the elliptic function, but from what I remember off-hand it seems that if you increase the speed of light, the orbital radius would increase as well, all other things being equal. I might be wrong though, and it depends on the boundary conditions as well. If I have time tonight I might plot it using Maple, and see what happens.
    It would increase, I didn't expect that!

    I don't want you to waste time for that either Markus, I don't think I would even understand the details of the calculus. Just a simple explanation would be great.

    I think you understand my question. Said differently, the effect of increasing the mc^2 of the Earth by a factor of 100 will be dependent on whether the mc^2 was increased by increasing m or by increasing c. In the example of the Earth and the satellite, increasing m might make the satellite fall, but not increasing c. Or at least the effect will be different.

    So when people say that in general relativity the charge is the energy, it doesn't tell the whole story; depending on what you do to change the energy you get a different result in terms of space curvature, geodesics, etc... anyways that's the question I was wondering...

    I am going on vacation tomorrow for one week. I hope we can continue this discussion then.

    Thanks again for your explanations, much appreciated.

    Nick.
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    Quote Originally Posted by Nic321 View Post

    I think you understand my question. Said differently, the effect of increasing the mc^2 of the Earth by a factor of 100 will be dependent on whether the mc^2 was increased by increasing m or by increasing c. In the example of the Earth and the satellite, increasing m might make the satellite fall, but not increasing c. Or at least the effect will be different.

    So when people say that in general relativity the charge is the energy, it doesn't tell the whole story; depending on what you do to change the energy you get a different result in terms of space curvature, geodesics, etc... anyways that's the question I was wondering.
    In other words, "don't bother with the math because I can't follow it, just give me a popscience explanation".

    OK, here it goes: the solutions (as I pointed out in an earlier link) depend in a complicated way (non-linear) on both AND on the Schwarzschild radius ,, of the central body. Basic algebra says that the influence of is much larger than the influence of because of the squaring.
    Last edited by Howard Roark; May 9th, 2014 at 11:45 AM.
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    lol ridiculous

    Anyways have a nice week everyone...

    I have downloaded some of Susskind's physics lectures on my laptop for the week hehehe...
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    Quote Originally Posted by Nic321 View Post
    lol ridiculous
    I dumbed it down as much as possible for you, you still didn't understand it. That's tough, I cannot dumb it down any lower.



    I have downloaded some of Susskind's physics lectures on my laptop for the week hehehe...
    Don't stress too much, Susskind is heavily into math, you will not get any of your desired popscience....Maybe you should start with a class in basic math? The barrier to entry to Susskind lectures is much higher than your demonstrated skills.
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    do you believe this guy is on his computer waiting for my answers. I should give my password to someone to make him think it's me lol pfff...
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    Quote Originally Posted by Nic321 View Post
    It would increase, I didn't expect that!
    I don't want you to waste time for that either Markus, I don't think I would even understand the details of the calculus. Just a simple explanation would be great.
    I did the explicit calculation as a little exercise, and if I am not mistaken or have made an error somewhere ( it was harder than I initially anticipated to figure this out ), the result I am getting is



    for the stable circular radius of a satellite of mass m and angular momentum L around a static, non-rotating central mass M in Schwarzschild space-time. If, all other things remaining equal, we increase the numerical value of c, the factor under the square root will get smaller ( inverse power of 4 ), whereas the leading factor in front of the bracket gets very much larger ( power of 2 ). The net effect is that the radius of the stable circular orbit will thus increase if one increases the speed of light.

    For a realistic scenario one would probably need to allow the central body to rotate, and repeat the calculation in Kerr space-time. The algebra then gets extremely tedious, so I won't be doing that on this occasion. Maybe someone else would like to take a shot at it on a rainy Sunday afternoon !

    Hope this helps to settle the original question.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Nic321 View Post
    It would increase, I didn't expect that!
    I don't want you to waste time for that either Markus, I don't think I would even understand the details of the calculus. Just a simple explanation would be great.
    I did the explicit calculation as a little exercise, and if I am not mistaken or have made an error somewhere ( it was harder than I initially anticipated to figure this out ), the result I am getting is



    for the stable circular radius of a satellite of mass m and angular momentum L around a static, non-rotating central mass M in Schwarzschild space-time.
    Markus,

    Your result doesn't seem right, see here for the correct derivation.

    the factor under the square root will get smaller ( inverse power of 4 )
    As an aside (not that it matters much since your formula doesn't seem right), the value under the square root gets bigger, not smaller. You must have had a rough day at the office :-)
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    Quote Originally Posted by xyzt View Post
    Your result doesn't seem right, see here for the correct derivation.
    Turns out I missed the factor m^2 under the square root, and was off by a factor ½ in the unit conversions :



    So those bits were errors on my side. I don't really know what they did in the Wiki article, but the above result matches exactly what is given in Taylor/Wheeler "Exploring Black Holes", page 4-29. It is also very close to the result for ( which is the stable orbit ) in the Wiki link, but it does seem to differ by some constant factors; that may well be down to a choice of units, since I used geometrized units throughout, and only converted back to standard SI units for the final result. I am not immediately sure how the Wiki link defines a, b and h, and what units they use; I am not saying it is wrong, but for the moment I choose to trust the textbook referenced above more than Wiki.

    As an aside (not that it matters much since your formula doesn't seem right), the value under the square root gets bigger, not smaller.
    Sorry, I meant to say the factor being the fraction under the square root.


    EDIT : I must be blind as a bat - in the Wiki article, we have just , then our formulas match up exactly. So I wasn't wrong, just off by a constant due to an error on my side. For some reason it is always the unit conversions that get me in the end
    Last edited by Markus Hanke; May 12th, 2014 at 02:10 AM.
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    Quote Originally Posted by xyzt View Post
    You must have had a rough day at the office :-)
    Let's not even go there
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    You must have had a rough day at the office :-)
    Let's not even go there
    Amazing thread - hope you guys can get the maths right.
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    Quote Originally Posted by Robittybob1 View Post
    Amazing thread - hope you guys can get the maths right.
    It's right now as it stands. Note that the qualitative answer hasn't changed ( increase c and the orbital radius will increase too ), I was merely off by a factor of ½ due to an error on my part.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    Your result doesn't seem right, see here for the correct derivation.
    Turns out I missed the factor m^2 under the square root, and was off by a factor ½ in the unit conversions :



    So those bits were errors on my side. I don't really know what they did in the Wiki article, but the above result matches exactly what is given in Taylor/Wheeler "Exploring Black Holes", page 4-29. It is also very close to the result for ( which is the stable orbit ) in the Wiki link, but it does seem to differ by some constant factors; that may well be down to a choice of units, since I used geometrized units throughout, and only converted back to standard SI units for the final result. I am not immediately sure how the Wiki link defines a, b and h, and what units they use; I am not saying it is wrong, but for the moment I choose to trust the textbook referenced above more than Wiki.

    As an aside (not that it matters much since your formula doesn't seem right), the value under the square root gets bigger, not smaller.
    Sorry, I meant to say the factor being the fraction under the square root.


    EDIT : I must be blind as a bat - in the Wiki article, we have just , then our formulas match up exactly. So I wasn't wrong, just off by a constant due to an error on my side. For some reason it is always the unit conversions that get me in the end
    You mean this. It is so nice to have a proper, sane thread, devoid of the "contributions" of the cranks :-)
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    Quote Originally Posted by Nic321 View Post
    Ok, but there has to be a deep reason why the constants keep their values across time and space. Understanding why these constants keep their values would tell a lot on how the universe works, how space time emerges etc...
    Quote Originally Posted by Nic321 View Post
    In any case, there has to be a mecanism that change those constants over time, in the very long term ( like in an inflationary universe). I have trouble buying the idea that the universe would necessarily have certain exact constants values that would suit our existence. There has to be some degree of evolution of the constants to explore all the possible values. So this means there has to be a mechanism that make these constants change
    No. The fundamental constants are not the parametisation of degrees of freedom of reality. For example, , , and together describe the scale of the standard units of measure relative to the fundamental scale of reality. This can be seen most clearly by combining , , and to form , , and , the Planck units of length, time, and mass respectively. Together, these Planck units are equivalent to , , and . That is, one can recover , , and from the Planck units, and therefore replace , , and by , , and as fundamental constants.

    Numerically, the Planck units are expressions of the fundamental units in terms of the corresponding standard units. But the Planck units ought to be able to stand alone as units to which all measurements are referred. In other words, the current standard units, though convenient, are redundant. In this case without other standard units, how does one specify the magnitude of the Planck units? In particular, how does one specify the magnitude of the Planck units in a way that any change in the magnitude becomes meaningful? Thus, the notion that the fundamental constants can be changed is meaningless when the true nature of the fundamental constants is considered.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    Quote Originally Posted by Markus Hanke View Post
    Most fundamental constants are interrelated
    , , and are independent.
    How do we know they are independent ?

    Being constants each, they could also be holding each other constant, therefore interrelated ?
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    Quote Originally Posted by Noa Drake View Post
    Quote Originally Posted by KJW View Post
    , , and are independent.
    How do we know they are independent ?
    Because one can derive the Planck units of length, time, and mass from them.

    The dimensions of , , and are:








    Inverting this set of three equations leads to the three Planck units:








    If , , and were not independent, then the equations describing their dimensions would not be invertible.
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    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    Your result doesn't seem right, see here for the correct derivation.
    Turns out I missed the factor m^2 under the square root, and was off by a factor ½ in the unit conversions :



    So those bits were errors on my side. I don't really know what they did in the Wiki article, but the above result matches exactly what is given in Taylor/Wheeler "Exploring Black Holes", page 4-29. It is also very close to the result for ( which is the stable orbit ) in the Wiki link, but it does seem to differ by some constant factors; that may well be down to a choice of units, since I used geometrized units throughout, and only converted back to standard SI units for the final result. I am not immediately sure how the Wiki link defines a, b and h, and what units they use; I am not saying it is wrong, but for the moment I choose to trust the textbook referenced above more than Wiki.

    As an aside (not that it matters much since your formula doesn't seem right), the value under the square root gets bigger, not smaller.
    Sorry, I meant to say the factor being the fraction under the square root.


    EDIT : I must be blind as a bat - in the Wiki article, we have just , then our formulas match up exactly. So I wasn't wrong, just off by a constant due to an error on my side. For some reason it is always the unit conversions that get me in the end
    Hi Markus,

    Thanks a lot for taking the time to educate neophits like me and xyzt, I can tell you we greatly appreciate your knowledge and wisdom.


    It is clear now, the orbital radius will increase with c, which means that in the example of the Earth and the satellite, if I get it right, the satellite will be ejected from its orbit if c is increased suddenly because it will have too much angular momentum.

    The equation is a bit surprising with the square root and the fact that the radicand is almost the inverse of the leading factor. And for the radicand to be positive, the term 12G... has to be smaller than one, which means that certain combinations of L/m and c cannot have an orbital radius.
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    Quote Originally Posted by KJW View Post
    Quote Originally Posted by Nic321 View Post
    Ok, but there has to be a deep reason why the constants keep their values across time and space. Understanding why these constants keep their values would tell a lot on how the universe works, how space time emerges etc...
    Quote Originally Posted by Nic321 View Post
    In any case, there has to be a mecanism that change those constants over time, in the very long term ( like in an inflationary universe). I have trouble buying the idea that the universe would necessarily have certain exact constants values that would suit our existence. There has to be some degree of evolution of the constants to explore all the possible values. So this means there has to be a mechanism that make these constants change
    No. The fundamental constants are not the parametisation of degrees of freedom of reality. For example, , , and together describe the scale of the standard units of measure relative to the fundamental scale of reality. This can be seen most clearly by combining , , and to form , , and , the Planck units of length, time, and mass respectively. Together, these Planck units are equivalent to , , and . That is, one can recover , , and from the Planck units, and therefore replace , , and by , , and as fundamental constants.

    Numerically, the Planck units are expressions of the fundamental units in terms of the corresponding standard units. But the Planck units ought to be able to stand alone as units to which all measurements are referred. In other words, the current standard units, though convenient, are redundant. In this case without other standard units, how does one specify the magnitude of the Planck units? In particular, how does one specify the magnitude of the Planck units in a way that any change in the magnitude becomes meaningful? Thus, the notion that the fundamental constants can be changed is meaningless when the true nature of the fundamental constants is considered.
    Ok, but by saying that you don't mean to say that the Planck constants would be necessarily the same in other universes for instance ( in an inflationary universe or whatever ). They could be different and produce different c, h and G.
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    Quote Originally Posted by KJW View Post
    Quote Originally Posted by Noa Drake View Post
    Quote Originally Posted by KJW View Post
    , , and are independent.
    How do we know they are independent ?
    Because one can derive the Planck units of length, time, and mass from them.

    The dimensions of , , and are:








    Inverting this set of three equations leads to the three Planck units:








    If , , and were not independent, then the equations describing their dimensions would not be invertible.
    I see, but we don't know what happens at the Planck scale. We don't really know what time is, what a dimension of space is etc... so maybe there is some complex phenomena occuring at this scale.

    Couldn't L, T and M be only simplified models of a much more complex reality? I don't know...
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    Quote Originally Posted by Nic321 View Post
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    Your result doesn't seem right, see here for the correct derivation.
    Turns out I missed the factor m^2 under the square root, and was off by a factor ½ in the unit conversions :



    So those bits were errors on my side. I don't really know what they did in the Wiki article, but the above result matches exactly what is given in Taylor/Wheeler "Exploring Black Holes", page 4-29. It is also very close to the result for ( which is the stable orbit ) in the Wiki link, but it does seem to differ by some constant factors; that may well be down to a choice of units, since I used geometrized units throughout, and only converted back to standard SI units for the final result. I am not immediately sure how the Wiki link defines a, b and h, and what units they use; I am not saying it is wrong, but for the moment I choose to trust the textbook referenced above more than Wiki.

    As an aside (not that it matters much since your formula doesn't seem right), the value under the square root gets bigger, not smaller.
    Sorry, I meant to say the factor being the fraction under the square root.


    EDIT : I must be blind as a bat - in the Wiki article, we have just , then our formulas match up exactly. So I wasn't wrong, just off by a constant due to an error on my side. For some reason it is always the unit conversions that get me in the end
    Hi Markus,

    Thanks a lot for taking the time to educate neophits like me and xyzt, I can tell you we greatly appreciate your knowledge and wisdom.
    While I appreciate Markus' posts, you should count only yourself as a "neophyte". Actually, you are more like an ignorant troll.




    The equation is a bit surprising with the square root and the fact that the radicand is almost the inverse of the leading factor. And for the radicand to be positive, the term 12G... has to be smaller than one, which means that certain combinations of L/m and c cannot have an orbital radius.
    Yep, the "radicand" :-)
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    Quote Originally Posted by Nic321 View Post
    Ok, but by saying that you don't mean to say that the Planck constants would be necessarily the same in other universes
    In what way could the Planck units be different in other universes? How do you compare the Planck units in one universe with the Planck units in another universe? Without comparing the Planck units with another set of units, how do you specify the magnitude of the Planck units in this universe? For example, the Planck length is specified in terms of the metre. But anything that affects the Planck length will also affect the metre so that the numerical value of the Planck length in metres will be unchanged. In other words, the notion that the Planck units can change is meaningless.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    Quote Originally Posted by Nic321 View Post
    Ok, but by saying that you don't mean to say that the Planck constants would be necessarily the same in other universes
    In what way could the Planck units be different in other universes? How do you compare the Planck units in one universe with the Planck units in another universe? Without comparing the Planck units with another set of units, how do you specify the magnitude of the Planck units in this universe? For example, the Planck length is specified in terms of the metre. But anything that affects the Planck length will also affect the metre so that the numerical value of the Planck length in metres will be unchanged. In other words, the notion that the Planck units can change is meaningless.
    I see well what you mean. But where I have a problem is with the fact that our universe appears to be fine-tuned for life, which would suggest that we are in a very special universe in the midst of a some sort of multiverse. In the video I posted above for instance Susskind explains that in the cosmic landscape of string theory, there could be a huge number of different universes.

    Do you see my point? How do you distinguish one universe from another? Wouldn't you try to compare the L, T, M from one universe to those of another?
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    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by Nic321 View Post
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    Your result doesn't seem right, see here for the correct derivation.
    Turns out I missed the factor m^2 under the square root, and was off by a factor ½ in the unit conversions :



    So those bits were errors on my side. I don't really know what they did in the Wiki article, but the above result matches exactly what is given in Taylor/Wheeler "Exploring Black Holes", page 4-29. It is also very close to the result for ( which is the stable orbit ) in the Wiki link, but it does seem to differ by some constant factors; that may well be down to a choice of units, since I used geometrized units throughout, and only converted back to standard SI units for the final result. I am not immediately sure how the Wiki link defines a, b and h, and what units they use; I am not saying it is wrong, but for the moment I choose to trust the textbook referenced above more than Wiki.

    As an aside (not that it matters much since your formula doesn't seem right), the value under the square root gets bigger, not smaller.
    Sorry, I meant to say the factor being the fraction under the square root.


    EDIT : I must be blind as a bat - in the Wiki article, we have just , then our formulas match up exactly. So I wasn't wrong, just off by a constant due to an error on my side. For some reason it is always the unit conversions that get me in the end
    Hi Markus,

    Thanks a lot for taking the time to educate neophits like me and xyzt, I can tell you we greatly appreciate your knowledge and wisdom.
    While I appreciate Markus' posts, you should count only yourself as a "neophyte". Actually, you are more like an ignorant troll.




    The equation is a bit surprising with the square root and the fact that the radicand is almost the inverse of the leading factor. And for the radicand to be positive, the term 12G... has to be smaller than one, which means that certain combinations of L/m and c cannot have an orbital radius.
    Yep, the "radicand" :-)
    radicand, dude, radicand:
    Definition of Radicand

    Learning basic math is fun, isn't it?
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  64. #63  
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    Quote Originally Posted by Nic321 View Post
    I see, but we don't know what happens at the Planck scale. We don't really know what time is, what a dimension of space is etc... so maybe there is some complex phenomena occuring at this scale.

    Couldn't L, T and M be only simplified models of a much more complex reality? I don't know...
    All this is irrelevant to the mathematics of obtaining the Planck units from the fundamental constants.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  65. #64  
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    Quote Originally Posted by Nic321 View Post
    I see well what you mean. But where I have a problem is with the fact that our universe appears to be fine-tuned for life, which would suggest that we are in a very special universe in the midst of a some sort of multiverse.
    It may well appear to be fine-tuned and special, but that may just be an appearance or even an extraordinary coincidence. Is there any evidence that there are any of the less "special" universes? One of the problems we face at present is that we are unable to explain a number of dimensionless constants, giving rise to the notion that these parametise different universes, with our universe being fine-tuned. But just because we can't explain these dimensionless constants doesn't mean that there is no explanation, especially given that we do not have a quantum theory of gravity.


    Quote Originally Posted by Nic321 View Post
    How do you distinguish one universe from another?
    Well, in one universe, my pen may be at one location, whereas in another universe, my pen may be at a slightly different location. Different universes even though they have the same laws of physics.


    Quote Originally Posted by Nic321 View Post
    Wouldn't you try to compare the L, T, M from one universe to those of another?
    No. Explain how one could perform such a comparison.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by Nic321 View Post
    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by Nic321 View Post
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    Your result doesn't seem right, see here for the correct derivation.
    Turns out I missed the factor m^2 under the square root, and was off by a factor ½ in the unit conversions :



    So those bits were errors on my side. I don't really know what they did in the Wiki article, but the above result matches exactly what is given in Taylor/Wheeler "Exploring Black Holes", page 4-29. It is also very close to the result for ( which is the stable orbit ) in the Wiki link, but it does seem to differ by some constant factors; that may well be down to a choice of units, since I used geometrized units throughout, and only converted back to standard SI units for the final result. I am not immediately sure how the Wiki link defines a, b and h, and what units they use; I am not saying it is wrong, but for the moment I choose to trust the textbook referenced above more than Wiki.

    As an aside (not that it matters much since your formula doesn't seem right), the value under the square root gets bigger, not smaller.
    Sorry, I meant to say the factor being the fraction under the square root.


    EDIT : I must be blind as a bat - in the Wiki article, we have just , then our formulas match up exactly. So I wasn't wrong, just off by a constant due to an error on my side. For some reason it is always the unit conversions that get me in the end
    Hi Markus,

    Thanks a lot for taking the time to educate neophits like me and xyzt, I can tell you we greatly appreciate your knowledge and wisdom.
    While I appreciate Markus' posts, you should count only yourself as a "neophyte". Actually, you are more like an ignorant troll.




    The equation is a bit surprising with the square root and the fact that the radicand is almost the inverse of the leading factor. And for the radicand to be positive, the term 12G... has to be smaller than one, which means that certain combinations of L/m and c cannot have an orbital radius.
    Yep, the "radicand" :-)
    radicand, dude, radicand:
    Definition of Radicand

    Learning basic math is fun, isn't it?
    I see, you are still trolling..
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    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by Nic321 View Post
    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by Nic321 View Post
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by xyzt View Post
    Your result doesn't seem right, see here for the correct derivation.
    Turns out I missed the factor m^2 under the square root, and was off by a factor ½ in the unit conversions :



    So those bits were errors on my side. I don't really know what they did in the Wiki article, but the above result matches exactly what is given in Taylor/Wheeler "Exploring Black Holes", page 4-29. It is also very close to the result for ( which is the stable orbit ) in the Wiki link, but it does seem to differ by some constant factors; that may well be down to a choice of units, since I used geometrized units throughout, and only converted back to standard SI units for the final result. I am not immediately sure how the Wiki link defines a, b and h, and what units they use; I am not saying it is wrong, but for the moment I choose to trust the textbook referenced above more than Wiki.

    As an aside (not that it matters much since your formula doesn't seem right), the value under the square root gets bigger, not smaller.
    Sorry, I meant to say the factor being the fraction under the square root.


    EDIT : I must be blind as a bat - in the Wiki article, we have just , then our formulas match up exactly. So I wasn't wrong, just off by a constant due to an error on my side. For some reason it is always the unit conversions that get me in the end
    Hi Markus,

    Thanks a lot for taking the time to educate neophits like me and xyzt, I can tell you we greatly appreciate your knowledge and wisdom.
    While I appreciate Markus' posts, you should count only yourself as a "neophyte". Actually, you are more like an ignorant troll.




    The equation is a bit surprising with the square root and the fact that the radicand is almost the inverse of the leading factor. And for the radicand to be positive, the term 12G... has to be smaller than one, which means that certain combinations of L/m and c cannot have an orbital radius.
    Yep, the "radicand" :-)
    radicand, dude, radicand:
    Definition of Radicand

    Learning basic math is fun, isn't it?
    I see, you are still trolling..
    I see, you don't see what to answer lol.. I can't believe you don't know that word but anyways.
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  68. #67  
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    Quote Originally Posted by KJW View Post
    Quote Originally Posted by Nic321 View Post
    I see well what you mean. But where I have a problem is with the fact that our universe appears to be fine-tuned for life, which would suggest that we are in a very special universe in the midst of a some sort of multiverse.
    It may well appear to be fine-tuned and special, but that may just be an appearance or even an extraordinary coincidence. Is there any evidence that there are any of the less "special" universes? One of the problems we face at present is that we are unable to explain a number of dimensionless constants, giving rise to the notion that these parametise different universes, with our universe being fine-tuned. But just because we can't explain these dimensionless constants doesn't mean that there is no explanation, especially given that we do not have a quantum theory of gravity.
    Well, some scientists seem to think there is some level of fine-tuning in the universe. I am not the one who brings up that idea. I don't find the idea particularily shocking, just like I wouldn't find the idea that there could be other planets where life could not arise shocking.

    You don't like that idea?

    Quote Originally Posted by Nic321 View Post
    How do you distinguish one universe from another?
    Well, in one universe, my pen may be at one location, whereas in another universe, my pen may be at a slightly different location. Different universes even though they have the same laws of physics.
    Ok, but why would all universes have the same laws of physics? Personally I find it hard to believe that the only thing that exist, the universe, or multiple universes, would all be suitable for life.

    For instance I read that in string theory, the landscape could have 10^500 different types of universes, although I don't know how they get to that number, by changing the shape of the Calaby-Yau manifold I guess I don't know.

    I don't know, maybe you don't like the idea of a multiverse. From what I've heard some scientists hate that idea.

    Quote Originally Posted by Nic321 View Post
    Wouldn't you try to compare the L, T, M from one universe to those of another?
    No. Explain how one could perform such a comparison.
    Well, I don't know, that what I was asking. Now I understand what you mean exactly, that all universes have exactly the same laws.
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