Einstein's space time is not a necessary component of reality!

[Doctordick]

Erasmus00,

 

You seem to be an intelligent and educated person; however, I think you expressed a "belief" which I do not think can be defended.

I believe that a universal "omnipresent now" cannot exist.

Since “simultaneity” can be defined for any specific reference frame but not in general, essentially, what you are saying is that there exists no “preferred” frame of reference demanded by the laws of physics. I would disagree with this; consider the frame of reference at rest with respect to the cosmic background radiation. That is very clearly a “preferred” frame of reference from the point of view of the existence of that radiation; however, some may argue that the existence of that radiation does not qualify as “a law of physics”.

 

That is a rather prejudice position to take but I will accept it from the perspective that it is in fact a consequence of our “local” measurements (perhaps, if we were elsewhere in the universe, the cosmic background might specify a different frame). Be that as it may, I think you ought to read a recent article by D. Salart, A. Baas, C. Branciard, N. Gisin, and H. Zbinden, from the Group of Applied Physics at the University of Geneva. (The following pdf file is available on the web.)

”Testing spooky action at a distance”

 

I think that experiment comes down to actually testing the existence of “preferred” frame of reference via consistency with known physical laws. It may be “spooky” with regard to Einstein's relativity, but it is entirely explicable from my proposed perspective. My presentation of relativity (both special and general) is totally in agreement with such “spooky” action without yielding any violation of a fixed velocity of light (so long as one uses a frame of reference at rest with the universe).

 

If you are interested, we can talk about it.

 

Have fun -- Dick

[modest]

It is not enough to define a preferred reference frame.

 

The question that may be raised in philosophical cosmology is whether or not this cosmic time constitutes an “absolute time” in the sense that Einstein rejected in his special theory of relativity. “Absolute time” and “relative time” may be defined in terms of the relation of simultaneity. If time is absolute, then this relation is two-termed, and is expressed by sentences of the form “x is simultaneous with y.” If time is relative, then the simultaneity relation is three-termed and is expressed by “x is simultaneous with y relative to z,” where z is the reference frame relative to which x and y are simultaneous. This suggests that the cosmic time posited by big bang cosmology is not absolute time, since the time measurements are made relative to the privileged reference frame. For example, the assertion that the age of the universe is about [13.7] billion years old is elliptical for the statement “relative to the privileged reference frame, the universe is [13.7] billion years old.”

 

Encyclopedia of time by Samuel L. Macey p.145

 

If a frame exists (preferred or not) where simultaneity is different from the CMB frame then simultaneity is not universal and not absolute, and of course such frames do exist.

 

~modest

 

EDIT: Dr. Dick, can you correctly do velocity addition with your Euclidean metric? If the answer is no (and I suspect it is) then what use does it have for us?

[Doctordick]

It is not enough to define a preferred reference frame.

You apparently did not read the title of this thead: “Einstein's space time is not a necessary component of reality!” The issue that you are side stepping is that there exists a very different approach to the issue Einstein's theory was developed to explain; one which does not require the concept of “space-time”.

 

Einstein's theory of special relativity (which, by the way, is called “special” because it applies only to transformations between frames moving at constant velocities with respect to one another) was developed to explain the problem generated by Maxwell's equation: i.e., the fact that Maxwell's equations violated the Galilean transformations which were derived from Euclidean geometry. The central issue of the problem was the fact that Maxwell's equations yielded a radiation solution with a fixed velocity. That occurs because electromagnetic phenomena (as defined by Maxwell's equations), in the absence of interactions, obeys a simple non-dispersive wave equation.

 

If you look at my fundamental equation, you should be able to comprehend that it also, sans interactions, is a simple non-dispersive wave equation and thus requires exactly the same type of fixed velocity as does Maxwell's equations. It can be seen as being exactly the form one would expect for the behavior of a Euclidean gas of massless point particles (energy being exactly proportional to momentum). The question then arises, does there exist a solution analogous to a three dimensional Euclidean gas of massive point particles and the answer is Yes. All one need do is consider a four dimensional collection of massless point particles, each and every one in a momentum quantized state in the same direction. If one is discussing a four dimensional Euclidean space, one then obtains an expression for the energy of the form [imath]E=|p|c = c\sqrt{p_x^2+p_y^2+p_x^2+p_\tau^2}[/imath] where [imath]p_\tau [/imath] has (for each and every element of interest) a quantized value.

 

If [imath]p_\tau[/imath] is quantized, then the uncertainty principal requires that the uncertainty in [imath]\tau[/imath] be infinite! If the uncertainty in [imath]\tau[/imath] is infinite, then, in the quantum mechanical solution to that equation, [imath]\tau[/imath] is not an observable coordinate and the solutions essentially amount to a gas of massive point particles in a Euclidean space of one fewer dimensions with the characteristic that the rest energy of any given point particle (rest meaning that the momentum of that point particle is entirely in the [imath]\tau[/imath] direction) is given exactly by [imath]p_\tau c[/imath], the quantized value times the velocity. It is a simple matter to identify that quantized momentum with “mc”, in effect obtaining [imath]E=mc^2[/imath].

 

Now, let us talk about the preferred “frame of reference” implied by Maxwell's equations which were, of course, originally discussed (and are actually still discussed) in a Euclidean frame where the velocity of that radiation is the same in every direction. That is, from the Galilean perspective, very definitely a “preferred frame of reference” and, it was that very issue which stood behind the Michelson-Morley experiments to determine the velocity of the earth through the aether. The problem was that the Michelson-Morley experiment yielded a null value which totally undermined the whole issue of Galilean relativity.

 

The solution of the problem, as seen by Lorentz and Fitzgerald, was the simple fact of Lorentz-Fitzgerald contraction, the apparent change in dimensions when one was not in that specific “preferred frame of reference” where the velocity of light was the same in every direction. That solution (when one considers the fact that the physical structure of all material objects of our experimental laboratories are essentially defined by electromagnetic phenomena) is actually quite a good solution; a solution, in fact, which does not require Einstein's space time continuum. The problem with such a solution is, the rest of the “laws of physics”; those which are not bound by Maxwell's equations: i.e., phenomena involving internal structures of massive entities. I have shown exactly the way around that problem; I have put before you a fundamental equation which I have shown to be required by any internally consistent explanation of anything and am in the process of showing anyone who is interested how that equation manages to reproduce the same fundamental equations of modern physics taken by physicists (in error) to require Einstein's space-time continuum.

If a frame exists (preferred or not) where simultaneity is different from the CMB frame then simultaneity is not universal and not absolute, and of course such frames do exist.

You, of all people here, should be cognizant of the fact your statement requires a definition of “simultaneity”. If you go to the actual facts, you will discover that all modern physics concepts of “simultaneity” include the supposed fact that the speed of light is the same in all directions. The problem with that supposition is the fact that it cannot be proved (that is exactly why Einstein put it forth as a “postulate”). If you read my presentation, you will discover that I do not make that postulate and yet obtain exactly the same results for the transformation between two frames (not at rest with respect to one another).

EDIT: Dr. Dick, can you correctly do velocity addition with your Euclidean metric? If the answer is no (and I suspect it is) then what use does it have for us?

Modest, I am not stupid. I have an earned Ph.D. in theoretical physics from a respected university and am fully aware of the experimental results which need to be addressed here. My results are entirely consistent with the standard transformations of modern physics, including velocity addition.

 

What I can do, and you should consider this to be significant, is generate quantum mechanically correct general relativistic transformations. The relativistic transformations in my picture are quite straight forward and do not even begin to have any problems with quantum mechanics (in essence, my whole approach is consistent with quantum mechanics from the word go).

 

See if you have the wherewithal to follow “An 'analytical-metaphysical' take on Special Relativity!” In particular, note the following extracted quote:

I have pointed out a number of times that, if the data belonging to a given observation could be divided into two (or more) sets having negligible influence on one another, those sets could be examined independently of one another: i.e., these collections would end up being constrained by exactly the same relationship which constrained the original universe. This is to say that these subsets (or “objects”) could be analyzed as a universes unto themselves; however, there is a subtle problem here: the fundamental equation was constrained (see appendix 3 of the original proof) to be valid only in the rest frame of the universe. The central issue here is that the two collections of elemental entities either have significant influence on one another or they do not. If they do not have any significant influence on one another, the constraint that the equation is only valid in the rest frame of “the universe” cannot be a valid constraint as either object may be considered to be a universe unto itself: i.e., the rest frame of one collection of elemental entities may not be the same as the rest frame of the other. The solution to this problem lies with the scaling of the geometry between the two systems: there must exist a consistent way of converting a solution in one system to a solution in the other independent of any influence between the two.

This is the very heart of the issue of transformations between different frames of reference and, unless you can understand the problem, you will never understand the solution.

 

Have fun -- Dick

[modest]

Thank you for such an engaging response Doctordick. I apologize that I have almost no time to properly formulate this reply or to properly consider what you have written. Your post deserves more time than I am able to give it, yet I do not want to be rude and leave it unanswered for another day...

It is not enough to define a preferred reference frame.

You apparently did not read the title of this thead: “Einstein's space time is not a necessary component of reality!” The issue that you are side stepping is that there exists a very different approach to the issue Einstein's theory was developed to explain; one which does not require the concept of “space-time”.

Certainly—if we can do physics without Einstein’s spacetime then, as you say, it can’t be considered necessary. At the same time, and hopefully you would agree, there are consequences of Einstein’s theory like the slowing of a clock’s timing or mass / energy equivalence which can’t be thrown out with the bathwater. I accept the possibility of different postulates and different interpretations besides ‘Einstein’s spacetime’ which are valid and lead to those same consequences.

 

I was not meaning to sidestep that issue. I should probably have been more clear that my previous post was not responding to the thread’s title, but rather to this...

I believe that a universal "omnipresent now" cannot exist.

Since “simultaneity” can be defined for any specific reference frame but not in general, essentially, what you are saying is that there exists no “preferred” frame of reference demanded by the laws of physics.

...where it seems to me that establishing a “universal, omnipresent now" requires more than defining a preferred reference frame. We can no doubt assert that some certain events are simultaneous in a preferred frame such as that of the CMB, but unless those events are also simultaneous in other valid inertial frames then a “universal, omnipresent now" has not been established. If we have to say “the events are simultaneous relative to the preferred reference frame” then by my reasoning they are still relative and not universal or absolute.

 

Einstein's theory of special relativity (which, by the way, is called “special” because it applies only to transformations between frames moving at constant velocities with respect to one another) was developed to explain the problem generated by Maxwell's equation: i.e., the fact that Maxwell's equations violated the Galilean transformations which were derived from Euclidean geometry. The central issue of the problem was the fact that Maxwell's equations yielded a radiation solution with a fixed velocity. That occurs because electromagnetic phenomena (as defined by Maxwell's equations), in the absence of interactions, obeys a simple non-dispersive wave equation.

 

Also central to the problem was that Michelson and Morley upheld the principle of relativity in 1887. It wasn’t until 5 years after that observation (and ce3rtainly because of that observation) that Lorentz developed his Lorentz invariant aether theory and likewise with Einstein’s SR. Theories prior to 1887 based on Maxwell’s equations did not have an invariant speed.

 

If you look at my fundamental equation, you should be able to comprehend that it also, sans interactions, is a simple non-dispersive wave equation and thus requires exactly the same type of fixed velocity as does Maxwell's equations. It can be seen as being exactly the form one would expect for the behavior of a Euclidean gas of massless point particles (energy being exactly proportional to momentum). , The question then arises, does there exist a solution analogous to a three dimensional Euclidean gas of massive point particles and the answer is Yes.

 

I don’t think I’m following what you’re saying. My knowledge of the physics of quantum and wave mechanics is probably inadequate. For massive and massless particles, I believe energy is proportional to p^2 and p respectively. I think that can be derived from kinetic energy....

massive:

[math]E=\frac{1}{2}mv^2 [/math]

[math]v=\frac{p}{m}[/math]

[math]E=\frac{p^2}{2m} [/math]

massless:

[math]E=\sqrt{m^2 c^4 + p^2 c^2}-m c^2[/math]

[math]m=0[/math]

[math]E=\sqrt{p^2c^2}=pc[/math]

Is that right...? Yeah, I agree with you, energy is proportional to momentum with free massless particles. I think you’ll find it’s quadratic with massive particles. But, I don’t know what Euclidean means as far as a Euclidean gas. And, I don’t follow what exactly you are getting at with this... though I am interested.

All one need do is consider a four dimensional collection of massless point particles, each and every one in a momentum quantized state in the same direction. If one is discussing a four dimensional Euclidean space, one then obtains an expression for the energy of the form [imath]E=|p|c = c\sqrt{p_x^2+p_y^2+p_x^2+p_\tau^2}[/imath] where [imath]p_\tau [/imath] has (for each and every element of interest) a quantized value.

And again, I don’t know what momentum in the tau direction could mean. I'll have to look at this when I'm not late for work. I, again, apologize.

 

******* EDIT ***********

 

The Klein–Gordon equation as far as energy / momentum relationship for relativistic massive and massless particles propagating in free space:

Relativistic free particle solution

 

The Klein–Gordon equation for a free particle can be written as

 

[math]

\mathbf{\nabla}^2\psi-\frac{1}{c^2}\frac{\partial^2}{\partial t^2}\psi

= \frac{m^2c^2}{\hbar^2}\psi

[/math]

 

with the same solution as in the non-relativistic case

 

[math]

\psi(\mathbf{r}, t) = e^{i(\mathbf{k}\cdot\mathbf{r}-\omega t)}

[/math]

 

except with the constraint

 

[math]

-k^2+\frac{\omega^2}{c^2}=\frac{m^2c^2}{\hbar^2}.

[/math]

 

Just as with the non-relativistic particle, we have for energy and momentum

 

[math]

\langle\mathbf{p}\rangle=\langle \psi |-i\hbar\mathbf{\nabla}|\psi\rangle = \hbar\mathbf{k},

[/math]

 

[math]

\langle E\rangle=\langle \psi |i\hbar\frac{\partial}{\partial t}|\psi\rangle = \hbar\omega.

[/math]

 

Except that now when we solve for k and ω and substitute into the constraint equation, we recover the relationship between energy and momentum for relativistic massive particles

 

[math]\left.\right.

\langle E \rangle^2=m^2c^4+\langle \mathbf{p} \rangle^2c^2.

[/math]

 

For massless particles, we may set ''m'' = 0 in the above equations. We then recover the relationship between energy and momentum for massless particles

 

[math]\left.\right.

\langle E \rangle=\langle |\mathbf{p}| \rangle c.

[/math]

 

http://en.wikipedia.org/wiki/Klein-Gordon_equation

 

 

******* END EDIT ***********

 

If [imath]p_\tau[/imath] is quantized, then the uncertainty principal requires that the uncertainty in [imath]\tau[/imath] be infinite! If the uncertainty in [imath]\tau[/imath] is infinite, then, in the quantum mechanical solution to that equation, [imath]\tau[/imath] is not an observable coordinate and the solutions essentially amount to a gas of massive point particles in a Euclidean space of one fewer dimensions with the characteristic that the rest energy of any given point particle (rest meaning that the momentum of that point particle is entirely in the [imath]\tau[/imath] direction) is given exactly by [imath]p_\tau c[/imath], the quantized value times the velocity. It is a simple matter to identify that quantized momentum with “mc”, in effect obtaining [imath]E=mc^2[/imath].

This is very thought-provoking. Do you know of any scientific literature that you could point me to that proposes quantizing momentum in the tau direction?

 

Now, let us talk about the preferred “frame of reference” implied by Maxwell's equations which were, of course, originally discussed (and are actually still discussed) in a Euclidean frame where the velocity of that radiation is the same in every direction. That is, from the Galilean perspective, very definitely a “preferred frame of reference” and, it was that very issue which stood behind the Michelson-Morley experiments to determine the velocity of the earth through the aether. The problem was that the Michelson-Morley experiment yielded a null value which totally undermined the whole issue of Galilean relativity.

 

:) we were thinking the same...

 

The solution of the problem, as seen by Lorentz and Fitzgerald, was the simple fact of Lorentz-Fitzgerald contraction, the apparent change in dimensions when one was not in that specific “preferred frame of reference” where the velocity of light was the same in every direction. That solution (when one considers the fact that the physical structure of all material objects of our experimental laboratories are essentially defined by electromagnetic phenomena) is actually quite a good solution; a solution, in fact, which does not require Einstein's space time continuum. The problem with such a solution is, the rest of the “laws of physics”; those which are not bound by Maxwell's equations: i.e., phenomena involving internal structures of massive entities.

I think you're alluding to the same thing I was earlier: the Lorentz aether theory,

Today LET is often treated as some sort of "Lorentzian" or "neo-Lorentzian" interpretation of special relativity. Introducing the effects of length contraction and time dilation in a "preferred" frame of reference leads to the Lorentz transformation and therefore it is not possible to distinguish between LET and SR by experiment. However, in LET the existence of an undetectable ether is assumed and the validity of the relativity principle seems to be only coincidental, which is one reason why SR is commonly preferred over LET.

 

Lorentz ether theory - Wikipedia, the free encyclopedia

 

I realize you're not advocating this theory, but the parallels are striking. Lorentz's aether theory is the very definition of ad hoc. For it to be a valid theory it must propose the principle of relativity and the invariant speed of light. So, deductively it is indistinguishable from SR except on a metaphysical level.

 

If there is no way to experimentally test the existence of a rest frame or a Lorentzian-like aether frame then Occam's razor should be applied.

 

I have shown exactly the way around that problem; I have put before you a fundamental equation which I have shown to be required by any internally consistent explanation of anything and am in the process of showing anyone who is interested how that equation manages to reproduce the same fundamental equations of modern physics taken by physicists (in error) to require Einstein's space-time continuum.

I'm now wondering what exactly you mean by "Einstein's space-time continuum". Do you mean Einstein's interpretation of the Lorentz transformations in his 1905 paper, or do you mean Minkowski spacetime. Or, perhaps you mean GR...? In any case, I would hope you agree that special relativity is an "internally consistent explanation" and that it is also consistent with observation.

 

Being the simplest explanation, I think physicist prefer it. Is it "necessary"? I think that depends on exactly what you mean by Einstein's spacetime. It is necessary that a clock's timing rate is affected by acceleration. It is necessary for muons created at high altitude from cosmic rays to reach the earth's surface. I do agree, however, there are alternative explanations for these predictions (such as the Lorentz aether theory linked above). Special relativity just happens to be the simplest way to derive relativistic effects. The effects are real. No matter how we derive e=mc^2, atom bombs still blow up.

 

If a frame exists (preferred or not) where simultaneity is different from the CMB frame then simultaneity is not universal and not absolute, and of course such frames do exist.

You, of all people here, should be cognizant of the fact your statement requires a definition of “simultaneity”. If you go to the actual facts, you will discover that all modern physics concepts of “simultaneity” include the supposed fact that the speed of light is the same in all directions. The problem with that supposition is the fact that it cannot be proved (that is exactly why Einstein put it forth as a “postulate”). If you read my presentation, you will discover that I do not make that postulate and yet obtain exactly the same results for the transformation between two frames (not at rest with respect to one another).

The existence of an invariant speed c can be derived without being postulated. From the principle of relativity and the homogeneity and isotropy of space these transformations can be derived:

[math]x = \frac{x' + vt'}{\sqrt{1+ K v^2}}[/math]

[math]t = \frac{t' + Kvx'}{\sqrt{1+ K v^2}}[/math]

It then becomes a matter of experiment to determine the value of K. If it is zero we get the Galilean transformations

[math]x = x' + vt' [/math]

[math]t = t'[/math]

If K is positive the result makes no physical sense and if K is negative we get the Lorentz transformations with an invariant speed c:

[math]\mathbf{ x=\frac{x' + vt'}{ \sqrt[]{1 -\frac{v^2}{c^2}} }} [/math]

[math]t=\mathbf{\frac{t' + \frac{vx'}{c^2}}{ \sqrt[]{1 -\frac{v^2}{c^2}}}}[/math]

Here are 3 papers from 1968, 1973, and 2008 which do this:

• Reciprocity principle and the Lorentz transformations (1968)
  
• Lorentz transformation from the first postulate.
  
• Faster-than-c signals, special relativity, and causality (section 2.1)
  

We do not need to postulate or prove that the speed of light is the same in all directions. The fact that there is an invariant speed arises from the principle of relativity. If that speed were infinite then we would live in a world of Galilean transformations and it is easy to prove that the invariant speed is not infinite.

 

Deriving the Lorentz transformations without postulating the invariant speed of light is a very impressive thing. When I have more time I will truly enjoy looking at your derivation.

 

EDIT: Dr. Dick, can you correctly do velocity addition with your Euclidean metric? If the answer is no (and I suspect it is) then what use does it have for us?

Modest, I am not stupid. I have an earned Ph.D. in theoretical physics from a respected university and am fully aware of the experimental results which need to be addressed here.

I am aware of your credentials, and more importantly, I am aware of your demonstrated ability with physics. I'm sorry if you took what I said as an implication otherwise. I am not an expert in physics. Aside from 2 years in college toward electrical engineering, I have no formal training in science. I am a hobbyist only, and I defer to your understanding, education, and abilities. If my question is stupid it is far more likely that I am asking a stupid question because I don't understand rather than implying the stupidity of you or your work.

 

By "Euclidean metric", I am referring to:

[math]c^2dt^2=dx^2+dy^2+dz^2+c^2d\tau^2[/math]

which, if I am not mistaken, you have advocated. Since tau is not an invariant, but an ordinary dimension, I cannot figure out how velocity addition can be successfully done with this metric. If I, modest, measure Bob at .5c and Bob measures Alice at .5c then at what do I measure Alice?

 

I can work out that problem using Minkowski spacetime, but I don't see how to get the correct relativistic results with the above metric. Judging by your response, I'm now convinced this is entirely due to my own shortcomings, but if it cannot be done then Einstein's spacetime is looking more necessary than it would otherwise.

 

~modest