Mentor

## can inertial reference frame have different sizes at least in theory?

 Quote by smm that is close, i am not very familiar of minkovskys matrix use, but i think the matrixs diagonal line would be K,K,K,K that is, locally time in reference frame that is K times bigger runs K times slower when the comparison is made between frames that have different size and are together in one place in same rest frame.
No problem, I can write it without using matrices as follows:
$T=kt$
$X=kx$
$Y=ky$
$Z=kz$

This is not a valid transformation between inertial frames. Consider Newton's 2nd law for a force, f, in the x direction:
$$m\frac{d^2 X}{dT^2} = m\frac{d^2(kx)}{d(kt)^2} = m\frac{k}{k^2} \frac{d^2 x}{dt^2} = \frac{1}{k} f$$

 yes the kinematics of larger reference frame would be different if its observed from smaller reference frame. i am not sure at all how the dynamics would change. i have guess that larger reference frame has K² times more energy and 1/K times slower energy transfer speed, and 1/K times smaller energy density. this comes from energy of harmonic oscillator that has energy K²kx²/2 if the string constant is same. how does different reference frames interact? is the larger reference frame "stiffer" since its time run slower or is it weaker and more fragile? i assumed above that slow time makes reference frame "stiffer". about kinematics: -if the K times larger reference frame is different in its natural unit length K times greater and time rate that is K times slower and there are no other changes, then -all time dependent functions would have transformation f(t)' = f(t/K) and all path dependent functions would have transformation f(l)'=f(Kl) -for example harmonic oscillator would oscillate K times slower and it would seem to dampen K times slower in larger reference frame. -all functions time derivatives if measured from normal reference frame, would be 1/K times slower the constant velocity would be invariant or same measured in both reference frames constant acceleration would be 1/K times slower in larger reference frame. i may do math mistake here, but would all higher order time derivatives of any time dependent function be then always 1/K times slower. i dont know how the higher order derivatives would seem to change, do they have some other rule than this. this could be if there are some other changes in larger reference frame than these two. about the dynamics: the different sized reference frame could have some other changes if these two changes arent enough to make the dynamics laws to work right. i have a rough guess that K times larger reference frame has always K² times more energy than normal reference frame in all energy forms (including mass?). for example nonrelativistic kinetic energy would be K²mv²/2 and the energy transfer rate could be K times slower, the energy density E/V K times smaller... this comes from dimensional analysis of energy of harmonic oscillator kx²/2 - if the string constant k is same then energy of harmonic oscillator is K² times larger. i dont have to take slowness of time into account since energy transfer is also 1/K times slower, right? odd thing about energy conservation is that if the energy is K² times larger and the reference frame does not exerience any forces during expansion, then this energy is free - or if small reference frame expands to larger one, it would have K² times more energy without actually doing any work. -but what are the limitations how the process can happen, is another question... it may be property of space that for example if reference frame moves long distances it may change larger proportional to the distance relative to local reference frame. this can happen if every rest frame has variation in natural unit length but moving rest frame does not change relative to another rest frame identically and therefore it seems to expand relative to local rest frame. -i mean if it is even possible to have inertial rest frames that have different unit length (and also time rate due to invariance of light velocity) hi mfb, about the selection of units- i dont mean the definition of units by using different unit systems, my question is about that the all physics or most of the physics change in reference frame such way that every physical propertys size iow space dimension is K times larger (and also their time rate is K times slower due to light speed invariance principle) than they are in normal reference frame. the change between units between two different sized reference frame together in same place would be t'=t/K time unit is K times longer (x',y',z)= 1/K (x,y,z) every space dimension unit is K times larger. and if the other frame is moving it also has relativistic changes. and if natural unit length varies from place to place inside same inertial reference frame, the change between units in different places would be (x,y,z) = K (x,y,z) and t remains same. also if the frame is moving, it has relativistic effects

Mentor
 Quote by smm how does different reference frames interact?
Reference frames don't interact. At least, I can't think of what you might mean by that.

Regarding the rest of your post. For every quantity of interest you could follow the process I did above to determine how it changes under the scale change. I don't really want to work through each one, so I am not going to check if each one is correct or not. It seems like a lot of effort when it is already clear that it is not an inertial frame. But don't just assume that you know how they should transform until you have carefully worked through several in detail.

 thanks for advice, ill look this through i mean the question how does two particles that are in two different sized frame of reference interact if they collide or have for example electromagnetic interaction. answer on this newton 2nd law issue: i think outside forces that act on particles in different sized reference frame has modification factor number in newton's 2nd law. i am not sure what the factor is- is it 1/K^3 or 1/K or something else
 i think its still inertial reference frame, but it have fixed modification in its kinematics and dynamics. i try to think that sized inertial reference frames are equal just like different moving reference frames in special relativity are equal - all natures laws are similar for inside observer. i have idea that reference frame is a physical property that gives also certain different dynamics to particles in that frame. -Different sized reference frames have different fixed laws of dynamics- similarly than in special relativity the relativistic frame of reference has fixed relativistic properties. but i am not sure what the dynamical properties are. i dont know would this require that this particle must be isolated from outside world somehow to hold its different properties. i dont know what happens if two different sized reference frames materia mix up together i think this idea or question is really worth of thinking because the reward is great: -if there can exist inertial reference frames that can have just any natural unit length, then for example in theory the whole observable universe can fit into size of one atom, if it has 10^40 times smaller reference frame whose laws of nature follow 10^40 times smaller scale (and 10^40 times faster time due to invariance of light)
 i add to the last "crazy sounding" sentense that if the mini-sized reference frame has also L^2 = 10^80 times less energy and therefore also 10^80 times less mass the idea of such things comes much more plausable. but can there be or is it possible in theory to have reference frames in different sizes?

Mentor
 Quote by smm i think its still inertial reference frame, but it have fixed modification in its kinematics and dynamics.
This is a self-contradictory claim. If it has any modification in its dynamics then it is not inertial.

 Quote by smm i try to think that sized inertial reference frames are equal just like different moving reference frames in special relativity are equal - all natures laws are similar for inside observer.
I proved above that Newton's 2nd law is different.

 quote: mfb You can just re-label all physical units and corresponding constants. If you do it consistently, you get the same physics again, but earth has a diameter of 1 meter, light needs 20ns to go around, or whatever. All observers will agree on the physical predictions, and all but you will agree that you use weird units. As you have to change the gravitational constant as well, the planck units will change their numerical value. You will get the same value for the diameter of earth, measured in planck units - there is no way to change that (with current physics). mfb, about the selection of units- i dont mean the definition of units by using different unit systems, my question is about that can the all physics or most of the physics change in reference frame such way that every physical propertys and law have size iow space dimension is K times larger (and also their time rate is K times slower due to light speed invariance principle) than they are in normal reference frame. -that is- can there be a reference frame at least in theory that follows natures laws in different length scale in all 3 dimensions (and also different time scale due to requirement that light speed is invariant) or shortly : can there be inertial reference frame that has different size or scale. there are no known phenomenon where this is true, i can think of that at first sight maybe , just maybe ultrarelativistic cosmic rays and hubbles law could involve this, and subatomic radiation (that is in these cases - expansion of reference frame) (-sorry for repetition)
 Recognitions: Homework Help Science Advisor If you modify some numerical values of physical constants like the gravitational constant, this is possible. But the result is just a different unit system.
 If I understand the OP well, then he asks if SR exhibits affine symmetry. The answer is: no. You can define an affine transformation of the spacetime, but it is not a symmetry. For instance, it does not preserve the speed of light. Changing scale also means changing energy, mass, temperature and other things. SR is symmetric only under isometric transformations. You could however change SR slightly, making a variable some parameter which is constant in normal SR that will reflect the changing scale. I wonder if it is not the 4-volume element.
 hi! in special relativity, particles that are "inside" relativistic reference frame, has more momentum and also more energy, when they still travel at limited speed near c - and this energy can be very large - i dont know does it have theoretical limit. this gives the motivation to my question. other fact in special relativity what gives motivation to this question is that it doesnt care what kind of object is "inside" moving inertial reference frame (but the object must be an isolated system) i am trying to think this way that the inertial reference frame is a "rigid" object that covers the space traveler "inside" it - and carries also all physical laws in it - and observer inside it will observe to be at rest and that all laws of nature are normal i could call this by another name, say "state of being at rest" , "rest-being", as i do below, i hope it clarify the issue i am talking about and my question in this thread is : can there exist "rest-being states" that have different size or alternatively said a different unit length or unit scale in all 3 dimensions at least in theory, even together at relative rest while this clearly is not known phenomenon in everyday physics now, if this "rigid state of being at rest" thing i called previously "inertial reference frame" has L times bigger unit length then all laws of nature follow bigger length scale - observer "inside the state of being at rest" still observes all natural laws to be normal. i mean if rest-being state can have different sizes, or should i say different scales. clearly - physics and astronomy does not know any "rest-states" that have larger unit length in all 3 dimensions. for example all atoms in whole universe or those the astronomers can see have similar properties and laws of physics , in other words they are in "same sized rest state" -at least when their relative velocity is near zero. also there is no known way that for example space traveler could change his "rest-being states" size, in other words, to expand or shrink his "rest-being state"- but according to special relativity he can at least accelerate his relative velocity and then have relative changes in his "rest-being state" in special relativity knows "rest states" that have different time rate and different lorenz contraction towards the direction of movement and you can draw time-space diagram and describe the line of simultaenity that changes its angle towards line of light speed, if the "rest states" relative velocity increases, right and general relativity describes something to happen to inertial "rest states" what produces gravitation but is it possible in theory, while it is not known phenomenon in every day physics and astronomy, to have "rest being state" that has different unit length? -i already made suggestion that L times larger rest-being state should have L times slower time to avoid situation that its light moves at superluminal speed. -other suggestion, what is more a guess, is that L times rest-being state would have L^2 times more relative energy if measured from 1 sized "rest being state" - and also relatively L times smaller rest-being state would have L^2 times less energy than 1-sized state. (i got this L^2 factor from harmonic oscillators energy 0.5kx^2 - but this factor must be same for all kind of energies) yes all suggestions makes changes to the rest-being states relative kinematics and dynamics measured by observer that is in 1-sized rest being state. -it seems that newtons I law would hold, (and in fact all constant velocities would be invariant) but newtons II law would have modification factor and also newtons III law would have modification factor when two particles that have different "rest-being state" interact with each other but if this "rest-being state" exists, then the observer inside it would still observe himself being in inertial reference frame... i mean if he measures only physics "inside" his rest-being state. but question still is open to me- can different sized "rest being states" exist at least in theory?
 hi! haell thank for the advice! i dont know about mathematics of affinity and other symmetries. have to check about these symmetries more i am not sure what do you mean. the wikipedia seems to have some information about these. i am not talking about selection of units, this is 3rd time i have to clarify this. do i use some wrong word or concept in this thread? i think this "rest-being state" is a good name of the thing i am thinking here. the "rest being -state" is state where observer measures all nature laws to be normal inside this state and also the observer measures to be at rest. this is the same thing, what "inertial reference frame" is in newtonian dynamics, right? the thing here below i am chasing is that what kind phenomenon of expansion of reference frame relative to other reference frame could be, how it could happen and does it need energy or not. (but i dont still know if it is possible to have such reference frames or "rest-being states") there are no known phenomenon where rest-being state can expand. Here i have some thoughts about modelling how the reference frame or rest-being state could expand. but i can make very simple model, where lights rest-being state can expand if the light moves long distance in same reference frame. i do this trick by using the fact that relativistic frame has lorenz contraction. i think this model is simple enough that you can follow it. if i make following new postulate to special relativity theory: postulate: -every inertial reference frame has variation in natural unit length such a way that s' = K(r) s0 where r is distance from origin and : dK/dr <0 k(0)=1 k(r)>0 that means that natural unit length decreases from 1 to 0 or some value between 0 and 1 when distance from origin increases. this postulate is totally independent from other postulates in special relativity, isnt it but i dont proof it at any way. i just make this new postulate to get desired result, (i have heard this phrase somewhere, i dont remember where :) ). (in fact i could speculate that hubble's law comes from such new phenomenon, then the function K or its linear approximation would be K(r) = (1+H/c)r ) - this is very small number if r < 0.5BLY, something like 1+ 0.75*10^-10 [1/ly]- i have thought this a bit but i dont know about cosmology well enough to say is this right - there are 10 different cosmological tests etc) this kind of reference frame is no longer eucledian, it looks like a grid observed through magnifying class. this postulate does not change any nature laws if they are measured in very small areas. now when light moves from origin to distant place, its rest being state remains same because in lights reference frame all distances are zero (here use the lorenz contraction). but local rest frames or rest-being states natural unit length decreases - and result is that lights rest-being state expands relative to local rest-being state. one curious feature in this model is that expansion of reference frame or rest-being demands absolutely no outside energy! that is because nothing happens in the lights own reference frame during lights journey. well this is only a model. i think i got the concept of lorenz contraction right. if the frame expands some how, what ever the phenomenon would be - and the two assumptions below are true: 1. L sized rest-being state has more energy than normal rest-being state 2. during expansion of rest being state the observer inside the state does not feel any internal forces at all then the conclusion is that when the rest-being state expands, it gets more energy without doing any work!
 Mentor This thread has degenerated into personal speculation, which is against Physics Forums Rules, to which everyone agrees when they register. I have closed the thread.