Struggling to think of an answer which doesn't admit to either trolling or ego stroking?
Lorentz invariance and the multiverse, possible or not?
- Thread starter quantum_wave
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I didn’t want to impose my questions on Masterov’s thread but my understanding of the responses from Tach and rpenner over there is that for both the SR postulates to be true in SR, the point of origin of an event like the flash of a spherical light wave front must move with the inertial frame along the axis of motion relative to all other inertial frames. This makes the physics the same in all frames and the math transforms a light sphere in one frame to a concentric light sphere in all frames. Do I have this straight?
Is it correct to say that the Doppler effect one would observe with sound waves where the frequency of the sound changes as the point of origin passes is also observed with light waves via the red and blue shifting, but the shape of the sound wave would still be spherical in all frames just like the spherical concentric light wave fronts?
Is it correct to say that the Doppler effect one would observe with sound waves where the frequency of the sound changes as the point of origin passes is also observed with light waves via the red and blue shifting, but the shape of the sound wave would still be spherical in all frames just like the spherical concentric light wave fronts?
The centre of the sphere is what moves with the chosen reference frame, and the definition of that centre will vary between different frames. It's not just about time dilation and space contraction, but about the relativity of simultaneity and time-ordering as well. For more info, please learn how to compute Lorentz transformations.
The sound isn't traveling at light speed, so no.
I am deluded enough to believe I understand the math and am simply visualizing how it portrays the SR effect in different frames. You can disparage me for that delusion and I won't take offense.
One small point about the spherical sound wave and an observer in motion relative to it. If that spherical wave could be observed in its full expanding volume by a moving observer, would it appear to be an oblate spheroid from his perspective?
It is a legitimate question that some one should be able confirm and put this issue behind for me. Would an object that has a fixed volume like a basket ball or even an expanding spherical sound wave expanding at the speed of sound (but not a light wave front expanding at the speed of light as CptBork pointed out) that is spherical in one observers frame (the rest frame) would appear as an oblate spheroid when viewed by an observer in motion relative to that frame.
My conclusion subject to input from a professional or subject to a link offered by anyone to the contrary:
The speed of the object relative to the speed of light would seem to determine how oblate it would appear to an observer whose motion is up to but not equal to the speed of light relative to the object at rest.
This is because the speed of light is impossible to achieve for anything other than light itself and therefore all Lorentz transformations in SR are done using the speed of light in the denominator and it is impossible for that relative speed to occur accept for light spheres themselves. As a result all light spheres transform spherically in all frames.
My question is, won’t all material objects (whose relative motion is less than the speed of light) appear as oblate spheroids where the “diameter” along the degree of freedom (say the X axis) in which the motion is occurring is length contracted to the moving observer, while there is no length contraction in perpendicular degrees of freedom along the Y and Z axes.
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A sphere of expanding light is a sphere in all inertial frames. A spherical object which is not made of light will only be spherical in its rest frame. However, due to the Terrell rotation effect it will still appear spherical to someone looking at it due to precise cancellations of effects because we see via light.
Motor Daddy
Valued Senior Member
That statement is not in accordance with the theory of relativity.
You can NOT length contract in one direction (the x axis) and not the other direction (y, and z axis) and still have a sphere. The measure of distance from the center of the sphere to the outer edge of the sphere is timeless, ie, the only way the outer edge of the sphere is a distance away from the center of the sphere is if the motion has already occurred in the past. There is no duration at that point, you are looking at a record of what ALREADY HAPPENED in time. There is no length contraction, and there is no time dilation, because there is no time interval at that point. It is a result! It's like looking at the results of a 1/4 mile car race. The race already occurred in the past, there is no time interval while looking at the results of a race that already occurred.
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Special Relativity of light spheres can be explained in my view by the following discussion.
My view is that the duration between any two events is the same for all parings of events that start at one universal freeze frame and end at a subsequent universal freeze frame, i.e. the motion that occurs between two freeze frames takes the same amount of time to occur everywhere in the universe in my pea brained view. Light has a finite speed which varies depending on the energy density of the medium through which it passes, so that makes the motion of light an event that is occurring in universal time just like any other event. You will see how this speculation would affect all of our observations.
A freeze frame says that all motion is stopped at the same universal time across the entire universe. If you are looking through a telescope at a distant planet and watching a rock roll down a hill when the freeze takes place, you are looking at the rock as it looked back in time. Since the freeze frame occurs everywhere at the same universal time and because you are living in universal time, the distant rolling rock is therefore rolling in delayed light time.
When the freeze frame is invoked and universal time stops, all motion including the motion of the rock and the motion of light waves in space stop frozen in place at the same universal instant.
Because you were watching time delayed events, the rock had long since stopped rolling by the time you were seeing it. When a freeze frame is invoked you have the imaginary ability to traverse the universe during the freeze frame. As you move time seems to be going forward as you experience the light waves because the visual history of the rolling rock event is captured in the traversing stream of light between you and the rock. So when you get to where the rock really is you find that it has moved from where it was while you were watching it through the telescope to where it was when the freeze frame was invoked. You realize that the entire universe is laid out before you and that the time delay is determined not only by the invariant speed of light, but also by the density of the medium through which the light travels between the rock and the observer.
People all over the universe could have been observing that rock and each one would have been looking at the light from it, but the rock has a real location and a real time while the observers see the light that has traveled for different durations and through different energy densities and so no two observers actually were seeing the rock in real universal time.
But there is a mathematical solution for the difference between all observers’ positions. All you need to know is the distance and the density of the medium between the observer and the rock. To the extent that both of those variables are measurable during the freeze frame, the math can perfectly describe the different perspectives at the instant of the freeze frame, in my pea brained view.
My view is that the duration between any two events is the same for all parings of events that start at one universal freeze frame and end at a subsequent universal freeze frame, i.e. the motion that occurs between two freeze frames takes the same amount of time to occur everywhere in the universe in my pea brained view. Light has a finite speed which varies depending on the energy density of the medium through which it passes, so that makes the motion of light an event that is occurring in universal time just like any other event. You will see how this speculation would affect all of our observations.
A freeze frame says that all motion is stopped at the same universal time across the entire universe. If you are looking through a telescope at a distant planet and watching a rock roll down a hill when the freeze takes place, you are looking at the rock as it looked back in time. Since the freeze frame occurs everywhere at the same universal time and because you are living in universal time, the distant rolling rock is therefore rolling in delayed light time.
When the freeze frame is invoked and universal time stops, all motion including the motion of the rock and the motion of light waves in space stop frozen in place at the same universal instant.
Because you were watching time delayed events, the rock had long since stopped rolling by the time you were seeing it. When a freeze frame is invoked you have the imaginary ability to traverse the universe during the freeze frame. As you move time seems to be going forward as you experience the light waves because the visual history of the rolling rock event is captured in the traversing stream of light between you and the rock. So when you get to where the rock really is you find that it has moved from where it was while you were watching it through the telescope to where it was when the freeze frame was invoked. You realize that the entire universe is laid out before you and that the time delay is determined not only by the invariant speed of light, but also by the density of the medium through which the light travels between the rock and the observer.
People all over the universe could have been observing that rock and each one would have been looking at the light from it, but the rock has a real location and a real time while the observers see the light that has traveled for different durations and through different energy densities and so no two observers actually were seeing the rock in real universal time.
But there is a mathematical solution for the difference between all observers’ positions. All you need to know is the distance and the density of the medium between the observer and the rock. To the extent that both of those variables are measurable during the freeze frame, the math can perfectly describe the different perspectives at the instant of the freeze frame, in my pea brained view.
If I imagine time is see compression of linked particles which are looped like twisted elastic bands. So IMO time is just compression. It rules out a lot of possibilities, but is much simpler in terms of physics. The bow shock of a moving sun for example is compressing the interval between particles, and that interval is looped. Linked conveyor belts are another way to imagine the phyiscs.
Correction: That statement is not in accordance with your understanding of relativity; which is extremely lacking.
I’ll spend some time describing the universe from my view and then will try to differentiate between that view and the multiverse views that are addressed in Mersini-Houghton’s paper.
Perfect Cosmological Principle
The universe that the freeze frame defined above (in my previous post) applies to is spatially infinite and has always existed (two of my postulates). Unless you pay special attention to the placement of objects you cannot distinguish one freeze frame from another, i.e. the universe on a grand scale looks approximately the same from all points in space and at all points in time. There is no edge, there is no center; matter and energy is present throughout in various densities that are continually fluctuating at all points in space as time passes.
The universe is referred to as shapeless and on a large scale it is has a fixed average energy density. That density fluctuates at all points in space because the universe is completely composed of wave energy in motion (one of my postulates). Wave energy is always conserved; energy cannot be created or destroyed.
The motion of wave energy occurs in accordance with natural processes and in compliance with invariant natural laws (I describe specific speculative processes and natural laws if scientific observations and data don't provide them). Wave motion is governed by limits and thresholds of energy density and energy density is defined as the amount of wave energy in an environment. Background wave energy, particle formation, particle negation, gravity, light, and natural processes govern the wave energy density.
The natural laws of the universe assure the perpetual presence of habitable environments where life can both be generated or to which life can migrate (postulates). Life that is generated and that finds a foothold in a hospitable environment can evolve in accordance with the invariant natural laws and change from the initial life form to more and more intelligent life forms (postulate).
That is the “perfect cosmological principle” that applies to my view of the universe. I know it goes beyond the current scientific definition of the cosmological principle and the perfect cosmological principle so this description is only my pea brained view.
Perfect Cosmological Principle
The universe that the freeze frame defined above (in my previous post) applies to is spatially infinite and has always existed (two of my postulates). Unless you pay special attention to the placement of objects you cannot distinguish one freeze frame from another, i.e. the universe on a grand scale looks approximately the same from all points in space and at all points in time. There is no edge, there is no center; matter and energy is present throughout in various densities that are continually fluctuating at all points in space as time passes.
The universe is referred to as shapeless and on a large scale it is has a fixed average energy density. That density fluctuates at all points in space because the universe is completely composed of wave energy in motion (one of my postulates). Wave energy is always conserved; energy cannot be created or destroyed.
The motion of wave energy occurs in accordance with natural processes and in compliance with invariant natural laws (I describe specific speculative processes and natural laws if scientific observations and data don't provide them). Wave motion is governed by limits and thresholds of energy density and energy density is defined as the amount of wave energy in an environment. Background wave energy, particle formation, particle negation, gravity, light, and natural processes govern the wave energy density.
The natural laws of the universe assure the perpetual presence of habitable environments where life can both be generated or to which life can migrate (postulates). Life that is generated and that finds a foothold in a hospitable environment can evolve in accordance with the invariant natural laws and change from the initial life form to more and more intelligent life forms (postulate).
That is the “perfect cosmological principle” that applies to my view of the universe. I know it goes beyond the current scientific definition of the cosmological principle and the perfect cosmological principle so this description is only my pea brained view.
It is in accordance with special relativity. Look for threads between Jack_ and I, as he claimed it was some internal contradiction of SR that it predicted such a thing. I explained to him why it is not.
Alternatively you could just do the Lorentz transformations yourself. Do on, why don't you apply a transformation to the following equation for a sphere of light expanding at c centred on the origin : $$x^{2}+y^{2}+z^{2} = (ct)^{2}$$. Actually, I'll do it for you and I'll do it in general SO(N,1) too!
Equation for a sphere centred on the origin of radius R : $$\mathbf{x}\cdot \mathbf{x} = R^{2}$$.
Set R = ct for photon sphere : $$\mathbf{x}\cdot \mathbf{x} = (ct)^{2}$$
Rearrange : $$-(ct)^{2} + \mathbf{x}\cdot \mathbf{x} = 0$$
Use Minkowski metric $$\eta_{ab}$$ and vectors $$x^{a} = (ct,\mathbf{x})$$ : $$\eta_{ab}x^{a}x^{b} = 0$$
Apply Lorentz transform, $$x^{a} \to y^{a} = \Lambda^{a}_{b}x^{b}$$ : $$\eta_{ab} y^{a}y^{b} = 0$$
Insert y definition, $$y^{a} = \Lambda^{a}_{b}x^{b}$$ : $$\eta_{ab} \Lambda^{a}_{c}x^{c} \Lambda^{b}_{d}x^{d} = 0$$
Use Minkowski invariance on LHS $$\eta_{ab} \Lambda^{a}_{c}\Lambda^{b}_{d} = \eta_{cd}$$ : $$\eta_{ab} \Lambda^{a}_{c}x^{c} \Lambda^{b}_{d}x^{d} = \eta_{cd} x^{c} x^{d} $$
Equate results : $$\eta_{cd} x^{c} x^{d} = \eta_{cd} y^{c} y^{d} = 0 $$
Thus the new Lorentz transformed coordinates satisfy the equation, an expanding photon sphere.
This is one of those counter intuitive results where intuition fails. You should really learn some relativity MD. How many more years you going to waste whining about something you don't understand?
Someone correct me if I'm wrong but that is saying that the math works and not that it corresponds precisely to reality.
Also, I have a question about the math. Would it be appropriate to refer to Minkowski spacetime as the coordinate system where the math works perfectly? Does it work just as well in flat spacetime and in curved spacetime, or does that question even make any sense?
Is flat spacetime the same as 3-D space plus time in Euclidean coordinates.
Also, I have a question about the math. Would it be appropriate to refer to Minkowski spacetime as the coordinate system where the math works perfectly? Does it work just as well in flat spacetime and in curved spacetime, or does that question even make any sense?
Is flat spacetime the same as 3-D space plus time in Euclidean coordinates.
Consider yourself corrected. Every experimental test devised exactly agrees (within experimental uncertainty) with the mathematical predictions of relativity.
No. Minkowski space (or flat space) is what the space is. You can chose to write it in whatever coordinates to like, for example cartesian, polar, cylindrical, curvilinear ...
Flat space = special relativity. Curved space = General relativity. GR requires quite a bit more work, but it essentially works the same way as SR.
I'm actually going to answer this...
Lets consider flat space in Cartesian coordinates. Euclidean flat space is where the metric tensor has signature $$(+,+,+,\ldots,+ )$$. i.e. it loos something like this: $$ ds^2 = dx^2 + dy^2 + dz^2 + \ldots$$. Minkowski signature space has signature $$(-,+,+,\ldots,+ )$$ where the minus sign is the time direction. The metric tensor is $$ ds^2 = -dt^2 + dx^2 + dy^2 + dz^2 + \ldots$$. Some people like to use the opposite signature $$(+,-,-,\ldots,- )$$ so the metric tensor is $$ ds^2 = dt^2 - dx^2 - dy^2 - dz^2 - \ldots$$ but really it's just convention.
So I would have been correct if I had said that the math works but doesn't correspond precisely to reality, it corresponds to reality within the limits of experimental uncertainty? I'll gladly use that phrasing.
And I'm not saying that general relativity is a bag of scabs or that Einstein's equations are not the best we have at the present. But I am likely to put more weight on finding the causes of the experimental uncertainty than someone who thinks that when the experimental uncertainty is resolved that general relativity will prove to be reality. To me the jury is still out on that.
So you are saying the Euclidean flat space has some baggage when it comes to today's consensus theories and it cannot be used to produce results that are as accurate as today's theories? I would probably agree with that even though I not sure what the baggage is, lol.
This is your choice to be intellectually dishonest, since without experimental disagreement there is no evidence for the proposition that the math doesn't correspond precisely to reality. Therefore your speculations are wholly unfounded and you are not beginning to address reality.
Mostly true but my argument is that there could be physical causes for the effects that are mathematically accounted for in GR and if that were the case then research and study would be applied. My statement was intellectually honest to that extent.
The taught laws of physics, as we now have them, are bare mathematical expressions of the experimentally perfect symmetries of reality. There is, as of yet, no wiggle room in physical observations to prefer any mechanism or "underlying reality" to the bare observed symmetries. Therefore any talk of "causes" are fact-free speculation, and only scientific to the extent that one develops the mathematics of ones speculative reality closer to the point where a confrontation between hypothesis and observation may be achieved. Where, sir, are your mathematics?
Motor Daddy
Valued Senior Member
I appreciate your perspective and certainly give you the medal for having a grasp on the math and science. I'm a pea brain and so when you point out that there is math behind all the taught physics I get the impression that I have missed something and have been wrong for all these years about the inconsistencies in the the math as it is taught when we quantify the macro and the micro observations. Also I must be missing where the math gives us the physics to explain the presence of matter, the physical cause for action at a distance and the cause of the Big Bang. Being a pea brain and missing all that in the math and physics that you say has no wiggle room is what I base my conclusion on that I am a deluded pea brain. I think we might be on the same page on that conclusion.
You can rest assured that my agenda is strictly speculation and not science and I am extremely clear on that. If you read my threads you would at least have a chance to appreciate that fact. My agenda consists of a personal hobby to have my own view of cosmology that is internally consistent and not inconsistent with observations and data. I call my speculation reasonable and responsible which excludes "God did it", "something from nothing", and "fairy dust". If you want to waste your time on me, and if you haven't familiarized yourself with my crap by actually reading the threads, get familiar enough to show where the math and those observations resolve the issues I bring up and feel free to contradict the speculations that I include in my view. Paragraphs full of LaTeX script don't impress me because I am of the belief that math can be made to say things that are not fact, not true, and are not compatible.
But please note that my speculations are about things that are not resolved by science and so if you don't like any given one of them just suggest a better speculation or point to the science. And even though I don't expect you to bother I will point out that I am one of those crack pots who, when you tell me of the grand theories out there, will remind you that all science is tentative and that theory is not fact and so if theories are incompatible there is an error in them. If you as a mathematician and physics teacher can't resolve the math then what chance does a layman have?
Otherwise, please note that this is a discussion with a pea brain taking place in Pseudoscience forum where a few of the professionals in the scientific community lower their standards with conduct aimed at disparagement of the individual instead of addressing the speculations because everyone knows we can't prove there aren't green spaghetti monsters holding up the surface of the moon. Why waste your time unless you want to join that select few professionals who find it relaxing in their spare time to wallow around in pseudoscience and disparage the animals here.