A Revolutionary Idea: Rethinking Time Measurement in Physics

[PFanalog57]

Could "Scooby Doo"syllablism correspond to "troll" phenomena?

A mathematical description of time probably has no physical interpretation, unless, as Dr. Dick explains, a lucid definition/understanding of time, can be agreed upon.

So if Einstein says that "the train arrives here at ten o'clock" he means that the pointing of the small hand of his clock to the ten and the arrival of the train are "simultaneous events"... where the clock and the event, are in close proximity.

This definition of time appears to be OK when defining time for the place where the clock is located, but it is insufficient for defining time for a series of events at different locations, i.e. to evaluate times of events occurring at locations remote from the clock.

If for a location A of space, there is a clock, with an observer, and the observer at A can determine the time values of events in the immediate proximity of A by observing the positions of the hands of the clock which are simultaneous with the events at location A.

If at another location in space, point B, with an identical clock, the observer at B can determine the time values in the immediate proximity of B. But the time of an event at A cannot compare to the time of an event at B since a common time for both A and B is yet to be defined.

According to Einstein, the time it takes a ray of light to travel from A to B equals the time it takes the ray to travel from B to A. Let the ray of light start at the A time "TA" from A to B, it arrives at the B time "TB" and is reflected back in the direction of A, where it arrives at the A time "T'A".



TB - TA = T'A - T'B

A "synchronous" definition of time is arrived at?

2AB/[T'A - TA] = c, the speed of light in vacuum.



Distance is a property between objects in space. Duration is a distance between events in time. Spacetime is a relational structure; The structure
of space is possibly a distributive lattice. A lattice is a
partially ordered set, closed under least upper and greatest lower
bounds.

Any lattice which is isomorphic to a collection of sets, closed
under complementation and intersection, is a Boolean
algebra.

Is it possible to derive Einstein's field equations
strictly in terms of quantum mechanical operators? using n-dimensional
cross sections of cotangent vectors?


What is needed is a tensor equation which is parallel
to "wave" equations described in terms of a covariant
d'Alembertian operator. An alternative description for the general
relativistic space-time, that allows for "compressional" waves,
rather than allowing only "transverse" waves.

 

[Doctordick]

An Ideal Clock in the Eucledian perspective.

I appologize to all as I apparently cannot post the gif diagrams essential to the clock design. Hurkyl's concern was answered by private mail. If anyone else is seriously interested, you know how to reach me.

Sorry about that -- Dick

 

[Hurkyl]

You should be able to attach a .gif to any post; but it may have to wait and be approved by Greg first.

 

[Doctordick]

Ideal Eucldian Clock -- Part I

You should be able to attach a .gif to any post; but it may have to wait and be approved by Greg first.

So here it is. I'll delete it if the gif files don't show up in a few days.

[size="+2"]Analysis of an Ideal Clock
[/size] by Richard D. Stafford, Ph.D.​

In the following, I will totally neglect microscopic phenomena except to assume that microscopic interactions exist and that these interactions, whatever they are, are capable of generating and maintaining the existence of objects whose structures are macroscopically stable over distances and times of interest. I will use the term "event" to refer to a general point on the line segment specifying the path of a microscopic entity being described in my geometry.

My clock will consist of two components: a mirror assembly and an oscillator. Both can be seen as macroscopic assemblies of events. The oscillator will have zero rest mass; therefore, every event which is part of the oscillator will be in a zero eigenstate¹ of momentum in the \tau direction (the oscillator can be seen as a macroscopic collection of photons). The mirror assembly will be massive: i.e., every event making up the mirror will be in a non zero eigenstate of rest mass; thus it also follows that every event making up the mirror assembly must be in a non zero eigenstate of momentum in the \tau direction.

Since every event involved in this discussion is momentum quantized in the \tau direction, the microscopic structure must be periodic in the \tau direction. This clearly requires that the macroscopic cross section of both structures perpendicular to \tau must be uniform and their extension in the \tau direction must be infinite. This being the case, a description of their three dimensional cross-section completely describes their macroscopic shape. Our "clock" will be defined to be the entity pictured below.

http://home.jam.rr.com/dicksfiles/clock.gif
​

This clock is further defined by the following constraints: all events making up the mirror assembly have |k_{\tau}| large and k_x, k_y, k_z negligible on a macroscopic scale. On the other hand, events making up the oscillator will have k_{\tau}\equiv0, non-negligible k_y and negligible k_x, k_z. Furthermore, k_y of the oscillator will be negligible with respect to k_y of the mirror. We are free to make these assertions as we are defining an entity and, in the absence of contradiction, anything is certainly possible.

First, the consequences of quantum mechanics must be included from the ground up. The fundamental interaction equation is a many body wave equation. Since we are neglecting microscopic phenomena except for the assumption that they maintain the macroscopic structure, at a macroscopic level we can look at the ray optics limit of the microscopic solutions². Now consider the relationship between momentum and velocity; in the ray optic limit, their directions are the same³. It follows that, in macroscopic terms, although every event has exactly the same speed through the geometry⁴, the mirror is moving parallel to the \tau axis while the oscillator is moving parallel to the y axis. Since our assembly is infinite and uniform in the \tau direction, motion in the \tau direction yields no changes in the structure of our clock. If we now postulate that microscopic interactions between the mirror and oscillator are capable of reversing the sign of the oscillator's momentum upon contact with the mirror, the oscillator will bounce back and forth between the legs of the mirror assembly. Our clock will clearly have a period of \frac{2L_0}{c}.

Since every event in the system described has non-negligible momentum only in the (y,\tau) plane, we can display all dynamic phenomena while considering only that plane. Thus, let us examine our clock as it appears in that (y,\tau) plane, paying particular attention to the associated velocity vectors. Notice that although no constraint has been imposed on the sign of the momentum of events making up the mirror, each event making up the mirror must have momentum either in the plus or minus \tau direction. As the sum of all events must maintain a coherent whole (by definition, our object is coherent over the time and space considered) we need only focus on the collection of events having the same sign. For the sake of graphic representation, I choose that sign to be positive.

In any case where the interactions necessary to maintain the existence of my entity are negligible⁵, we can conclude that the velocity of the mirror (or those components we have focused on) is exactly c in the positive \tau direction⁶.

Following is a \tau,\,y cut of our clock at the midpoint of the oscillator perpendicular to the x,z plane:

http://home.jam.rr.com/dicksfiles/restcloc.gif
​

Note that T, the period of our clock, is identical to 1/c times the distance the mirror moves in the \tau direction during one clock cycle. Although actual position in the \tau direction is meaningless, (as the entire object is infinite and uniform in that direction), our clock is actually measuring displacement of the mirror over time in that direction: i.e., we can infer that the mirror has moved a distance 2L₀ in the \tau direction during one complete cycle.

Our mechanism is certainly analogous to a clock since it will keep time if we can count the number of times the oscillator bounces back and forth. Furthermore, the image is clearly that of a massless object (a coherent pulse of photons?) bouncing back and forth between two reflective surfaces of a massive mirror, the common construction of an accurate clock under the conventional physics viewpoint.

{Part II will follow below!}

 

[Hurkyl]

There should be a "manage attachments" button when you post a new reply; that will attach them if you don't want to link them.

 

[Doctordick]

Ideal Eucldian Clock --- Part II

Now let us consider an identical moving clock. In this case, k_y of the mirror is no longer negligible.

http://home.jam.rr.com/dicksfiles/movecloc.gif
​

Since all objects are uniform and infinite in the \tau direction, we may suppress drawing the objects themselves. Instead, we may deal entirely with the displacement vectors (\vec{V}c). It should be clear that these vectors contain all relevant information needed to predict the time evolution of our device. It is only necessary to remember that anytime the displacement vectors lead to identical (x,y,z) coordinates, microscopic interactions can occur between our macroscopic objects (because all macroscopic objects are infinite and uniform in the \tau direction). Please note that, in this particular case, x and z of every point in the picture is always identical so we need only concern our selves with the y coordinate of the displacement vectors.

http://home.jam.rr.com/dicksfiles/clocvect.gif
​

Note that the length of the moving clock is shown to be L'. This has been done because we know that the geometry must yield (by construction) a result totally consistent with the Lorenz contracted macroscopic solution if interactions with the rest of the universe may be neglected: i.e., when we solve the microscopic problem in the moving clocks system we want the length of the clock (when transformed into the original rest system) to be L₀. Only in the case where we can set the length (as seen from the rest system) to be L' can we call the clocks identical. This will require L'=L_0\sqrt{1-\beta^2}, where \beta is defined to be the sine of the angle between the \tau axis and the path of the clock⁷ Since all velocities are c, it follows directly that d₁ + d₂ = S.

Notice that the following geometric figure is embedded in the previous diagram.

http://home.jam.rr.com/dicksfiles/showdiog.gif
​

Once again we discover that one clock cycle measures exactly the length of time it takes the mirror to move the distance 2L₀ in the \tau direction. Although our clock was designed to measure time, it appears that what is actually being measured is inferred displacement in the \tau direction.

At this point it seems quite rational to point out that no one in the history of the world has ever been able to create a real manufactured device which will actually measure time. It can not be done because, although it is an absolute law that interactions can only occur between objects which exist at the same time, time can not be specifed absolutely as it is a relavistic thing which depends on your coordinate system). All so called clocks actually measure what a modern physicist calls proper time. He is able to define time only in his own rest frame. In that case dx = dy = dz = 0 and he can call what the clock measures "time" as, in that case and that case only, the two parameters (\tau and t) are universally proportional. It should be noted that all clocks measure "proper time" exactly, even when in an arbitrarily accelerated frame! I have always found it rather strange that this fact was never pointed out to me during my graduate studies. It seems to me to be a very powerful statement.

End Notes
[size="-1"]

1. David Park, Introduction to the Quantum Theory, McGraw-Hill, Inc., NY, 1964, p.67.
2. Herbert Goldstein, Ph.D., Classical Mechanics, Addison-Wesley Publishing Co. Inc., Reading, Mass., 1959, p. 312.
3. Messiah, Quantum Mechanics, John Wiley and Sons, Inc., New York, 1966, p. 55.
4. I will use c to represent this velocity though I can show that there is a serious assumption in its actual value which we might discuss later.
5. The interactions are negligible if I can consider any subset of events making up the mirror as objects: i.e., the subsets form an analyzable universe unto themselves.
6. It can be shown that inclusion of these interactions will give rise to effects commonly attributed to general relativity.
7. This forces the apparent velocity of the clock to be beta times c.
[/size]

Have fun -- Dick

 

[Doctordick]

There should be a "manage attachments" button when you post a new reply; that will attach them if you don't want to link them.

Yes, I see it now. It didn't occur to me that the part II should be thought of as an attachment. Live and learn.

Thanks -- Dick

 

[Doctordick]

Though very few seem to be much interested in criticizing my alternate coordinate system for examining relativistic phenomena, for those who do have some interest in the perspective, I have managed to get you access to those gif files associated with the "Ideal Clock" design (evidently direct image posting is off limits). They appear as URLs which, if you click on them, will open a window containing the graphic.

There have been a lot of comments on this forum about speeds in excess of the speed of light. With regard to that, my representation makes the issue quite clear. As time is not a coordinate axis but rather a path length measurement, measuring it is a completely local phenomena and (as a specific numerical measurement) is only meaningful to the observer himself. On the other hand, the fact that things must exist at the "same time" in order to interact is still an absolute universal rule.

What the above means is that time has once again achieved the role it played in Newtonian mechanics: it is fundamentally a parameter specified by the observer to denote the distribution of events which he regards as simultaneous. Please note that all scientists familiar with relativity have made much of the fact that this can always be done without violating causality: i.e., simultaneity is in the eye of the beholder.

Since time is now merely a parameter of motion, if one wants to look at a set of interacting events over time (in their personal reference frame), they can construct exactly the same kind of diagram common to freshman physics analysis of motion: i.e., introduce time as a dimension on graphic representation of the motion.

My exposition on an ideal clock above is a good practice example to see what I am talking about. The most serious difficulty is that one cannot exclude the \tau axis as its existence always has profound consequences. This means that the simplest diagram one can create has three dimensions, x, \tau and t. What is important here is that, since time is a measure of path length, moving rapidly perpendicular to \tau makes your x motion a significant component of your change in time: i.e., the faster you go, the more quickly you go into the future (as compared to the reading on your own clock).

As an aside, the twin paradox is still resolved by the inclusion of acceleration (which would fall into the category of general relativity) which I won't go into at the moment. If anyone has any questions about it, I will go into the representation of general relativistic phenomena from this perspective; however, you should make an attempt to understand special relativistic phenomena from this perspective first.

The great power of my perspective is that it reinstates the concept of "simultaneous" collapse of the wave function in quantum mechanics, another phenomena which is in the eye of the beholder. The collapse of the wave function occurs when the observer knows what the outcome of the situation is. Just as time is a local construct conceived of by the observer, the wave function describing a phenomena is also a local construct devised by the observer.

That is exactly why a covariant representation of quantum mechanics is so involved; the wave function describing the expectations of the observer is no more universal than is the specification of simultaneity as seen by the observer. Easy conversion is only possible when d\tau and dt are linearly related to one another (special relativity). What my geometry does is to make representation of relativisticly correct set of distributed interactions easy to display from the observers perspective (well, at least somewhat easy).

Have fun -- Dick

 

[Antonio Lao]

Doctordick:On the other hand, the fact that things must exist at the "same time" in order to interact is still an absolute universal rule.

Only interaction by direct physical contact requires "same time." Interaction by quanta of force field is limited by light speed.

 

[Doctordick]

Relativistic Quantum Mechanics!

Hi Russell,

I have just finished learning latex code and was going through my old posts correcting what I put down to my intentions and decided I should respond to your post.

According to Einstein, the time it takes a ray of light to travel from A to B equals the time it takes the ray to travel from B to A. Let the ray of light start at the A time "TA" from A to B, it arrives at the B time "TB" and is reflected back in the direction of A, where it arrives at the A time "T'A".

TB - TA = T'A - T'B

A "synchronous" definition of time is arrived at?

2AB/[T'A - TA] = c, the speed of light in vacuum.

There is nothing wrong with such an approach at all except that it presumes there exists no special coordinate system. This perspective is rather all pervading even though, in the final analysis it is a mentally compartmentalized position. Certainly the distant stars provide a reference for a "center of momentum" coordinate system as special. It is clear that it would be quite reasonable to do calculations in a frame not rotating with respect with those distant stars (particularly if your interest was the orbits of the planets of the solar system). Now if they were to do so, it is clear that they would not find the speed of light on the Earth to the west to be the same as the speed of light to the east as they would be moving in their chosen reference frame.

Not a serious issue, except when one is trying to get down to fundamentals. If one wants to be absolutely correct, these kinds of issues must be thought about.

Is it possible to derive Einstein's field equations
strictly in terms of quantum mechanical operators?

It certainly is as I have done it (in essense anyway as my coordinate system is quite different from his). I need to make a slight intellectual correction to that statement: except for the fact that my results and Einstein's are slightly different. Who has made the error is still an open question as the required experiment to tell the difference is beyond current technology.

using n-dimensional
cross sections of cotangent vectors?

No, that is not the way I did it.

What is needed is a tensor equation which is parallel
to "wave" equations described in terms of a covariant d'Alembertian operator. An alternative description for the general relativistic space-time, that allows for "compressional" waves, rather than allowing only "transverse" waves.

Is that an opinion or a fact? If it is a fact, then I would like to see your derivation of general relativistic quantum mechanics. If it is not a fact, then it is only an opinion.

If you wish, I will give you my derivation of general relativistic quantum mechanics. But, before I do so, I need to know your education as without that knowledge I would have to start with freshman physics.

Have fun -- Dick

 

[Doctordick]

Only interaction by direct physical contact requires "same time." Interaction by quanta of force field is limited by light speed.

You are presuming your theory of "interaction by quanta of force" is correct. If you express the presumed interactions directly (that is, creation of the interacting quanta as an event and the effect of that interacting quanta as a second event) then each of those events occur at exactly the same time as either the causing event or the consequence event. It is your error to presume there is no difference between the two events.

Have fun -- Dick

 

[PFanalog57]

If you wish, I will give you my derivation of general relativistic quantum mechanics. But, before I do so, I need to know your education as without that knowledge I would have to start with freshman physics.

Have fun -- Dick

I am a part time college student of electrical engineering, age 42. I have taken all of the prerequisite "calculus" courses along with self study.

Your derivation of general relativistc quantum mechanics sounds very interesting.

Please proceed.

 

[Doctordick]

I am a part time college student of electrical engineering, age 42. I have taken all of the prerequisite "calculus" courses along with self study.

Your derivation of general relativistc quantum mechanics sounds very interesting.

Please proceed.

Ok, the first step is for you to tell me if you can follow my post #3 on the thread:

https://www.physicsforums.com/showthread.php?t=23266

If you have had no more than the prerequisite "calculus" courses, you may have difficulty following the derivation. Please post your responses to that post on that thread. I will do my best to clarify any problems you have. Once you accept the fact that the equation is fundamental, I will show you how to solve it step by step.

Have fun -- Dick

 

[PFanalog57]

Is that an opinion or a fact? If it is a fact, then I would like to see your derivation of general relativistic quantum mechanics. If it is not a fact, then it is only an opinion.

In a Schwarzschild spacetime via an analogue of the Schwarzschild spacetime of the Rindler vacuum state, for which static observers detect no particles, the expected stress-energy tensor becomes singular on two distinct portions of the intersecting null planes. This is known as the Hartle-Hawking vacuum, and the vacuum state will become a thermal state with respect to the notion of time translations with temperature T = hbar*c^3 / 8pi*k*G*M .

The vacuum state gives rise to a generalized entropy law, where the entropy S' never decreases:

S' = S_m + A/4

The area of a spacetime surface and the maximum amount of information contained in a finite region of space, cannot be greater than one quarter of the area in Planck units. Spin networks can describe the quantum geometry of space at the intersection of horizon boundaries, where the spin networks intersect with the boundary at a finite number of points.

There is a finite amount of energy contained by a given region of spacetime. A finite amount of information. A finite number of quantum phase entanglements and random fluctuations.

A phenomenon is random if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions.

The Hawking-Unruh effect is therefore the consequence of the noise spectrum for a massless scalar field along an accelerated trajectory in Minkowski space. It would appear to be a Fermi-Dirac form. The Unruh effect then becomes an integral part of a quantum field theory.


If the universe is closed, the "information" or entangled quantum states cannot leak out of the closed system. So the density of entangled quantum states, continually increases, as the entropy must always increase. While to us, it is interpreted as entropy or lost information, it is actually recombined information, to the universe. Shannon entropy.

Spacetime Memory = Compression Waves = Interpretation of Increased Entropy = Shannon entropy.


Einstein's equation basically says

Einstein Tensor [G] = Stress-Energy Tensor [T]

[spacetime geometry] determines [matter-energy's path] = geodesic.

[Matter-energy] determines [spacetime geometry] = non-Euclidean geometry.

.
Conservation of momentum energy is explained as an automatic consequence of the zero boundary of a boundary. Where conservation of energy-momentum means no creation or destruction of energy momentum in a 4D region of spacetime [4D cube] The integral of "creation events" i.e. the integral of d*T for energy momentum, over the 4D region is required to be zero, and gives the conservation of momentum energy. The mathematical machinery for identically meeting the conservation laws is the boundary of a boundary equals zero.

[spacetime tells mass]<==[geodesic]==>[mass tells spacetime]

An object following a geodesic has no unbalanced forces acting on it. Its energy-momentum is a constant. In order for the object to deviate from the geodesic, it must be accelerated. Energy must be expended, for example, its rocket boosters could fire, or an outside force like a meteor impact .


Waves are ripples in a basic medium. Einstein explains that the ether is unecessary as a medium, so the ripples are vibrations of the vacuum itself.

As the ripples intersect with each other, it becomes a domino effect with the ripples continually increasing in density. Very similar to taking a penny and doubling it as an iterative sequence.

2, 4, 8, 16, 32, 64, 128, 256, ... 2^n

Since the ripples are increasing in density they are "compressed" .

Actually, spacetime can proceed in discrete steps, yet, still be continuous[causally connected].

[density 1]--->[density 2]--->[density 3]---> ... --->[density n]


Quantum mechanics leads to the realization that all matter-energy can be explained in terms of "waves". In a confined region(i.e. a closed universe or a black hole) the waves exists as STANDING WAVES In a closed system, the entropy never decreases.

The analogy with black holes is interesting with the caveat that if there is nothing outside the universe, then it cannot be radiating energy outside itself as black holes are explained to be. So the amount of information i.e. "quantum states" in the universe is increasing. It is Shannon entropy, to an information processor with huge computational capabilities.

 

[Antonio Lao]

Doctordick,

The events happen in spacetime. The speed of traveling in space and the speed of traveling in time are related. These combined motions always equal the speed of light. If the interaction go faster in space then it will slow down in time, vice versa. No particle can travels greater than c in space, only light can do that. When light is traveling at exactly c in space then its speed in time is zero. Light does not age and time stands still.

 

[Doctordick]

Doctordick,

The events happen in spacetime. The speed of traveling in space and the speed of traveling in time are related. These combined motions always equal the speed of light. If the interaction go faster in space then it will slow down in time, vice versa. No particle can travels greater than c in space, only light can do that. When light is traveling at exactly c in space then its speed in time is zero. Light does not age and time stands still.

Please define exactly what you mean by "speed"!

 

[KingNothing]

I think you know what speed is. He's not talkin 'bout meth.

 

[PFanalog57]

This appears to be Dr. Stafford's definition of the problem with "time":

http://home.jam.rr.com/dicksfiles/flaw/Fatalfla.htm

The fundamental problem is two very different concepts of time. One concept of time is the idea that there is a state called the present which divides the universe into two different realms: the past which cannot be changed from the future which cannot be exactly known. The second concept of time is that it is the reading off a clock. These concepts are fundamentally inconsistent with one another.

Two issues ignored by the scientific community should be looked at very closely here. First, any competent physicists knows that it is impossible to construct a device which will provide a universal division between past and future for all possible reference frames. This being the case, they simply ignore that concept of time as being of no scientific significance. Quantum mechanics, on the other hand, seriously confronts that concept.

The second issue is the fact that all clocks are dynamic physical entities controlled by the laws of physics. Since the fundamental axiom of relativity is that the laws of physics are not frame dependent, the readings on a clock cannot possibly be frame dependent! Note that the only measure in the theory of relativity which is totally independent of the reference frame is Einstein's invariant interval which, as luck would have it, is exactly what all clocks measure. Scientists avoid thinking about this issue by placing their reference clocks in specific reference frames as if these frames are of special significance.

Time is a sequence, or interval, separating events on a "timeline/worldline". It is governed/determined by the laws of physics, it is not of itself a law of physics, since it is a measurement. Then again, c is invariant!

There can be no preferred frame of reference.

Space-time becomes Euclidean as distance between two arbitrarily different "frames" becomes very small. So two events become simultaneous as their space-time separation goes to zero.

Dr. Einstein's theory is still correct.

 

[Doctordick]

Dr. Einstein's theory is still correct.

I am glad you are so sure of that! I think you just find my work to be beyond your comprehension; as I suspect, so is Dr. Einstein's.

Have fun -- Dick

 

[PFanalog57]

I am glad you are so sure of that! I think you just find my work to be beyond your comprehension; as I suspect, so is Dr. Einstein's.

Have fun -- Dick

Thank you for the vote of confidence Dr. D.

A person can perform an experiment in a reference frame traveling at a velocity that is a significant fraction of the velocity of light or in a frame traveling at a low velocity. The results of the experiment will be the same at both reference systems.

There is no preferred frame for systems traveling at a constant relative velocity.

So what the heck do you mean? when you say:

Scientists avoid thinking about this issue by placing their reference clocks in specific reference frames as if these frames are of special significance.

 

[Netme]

Time has infinite dimensions. We live in our own dimension of time as do atoms and planets the universe and so on.

 

[Antonio Lao]

Doctordick,

My general definition of "speed" is rate of change of something with respect to something else. The something else is assumed not changing in any sense of the word. In other words, the something else takes the value of zero. This is the definition of a derivative in calculus.

This "not changing" is not the same as what we mean by a "constant." Constant is a value for all time (past, present, future).

 

[Doctordick]

I think you are trying to muddy the waters.

Doctordick,

My general definition of "speed" is rate of change of something with respect to something else. The something else is assumed not changing in any sense of the word. In other words, the something else takes the value of zero. This is the definition of a derivative in calculus.

This "not changing" is not the same as what we mean by a "constant." Constant is a value for all time (past, present, future).

Then I would presume you would find a reference to the "speed of the roof of my house" to be a very reasonable use of the term? Or is it rather that you don't want to confront the issue of exactly what you mean by "time"? I have a feeling it is the latter.

Have fun -- Dick

 

[Doctordick]

Time has infinite dimensions. We live in our own dimension of time as do atoms and planets the universe and so on.

I suspect you are not interested in logical thought. You are using the word "dimensions" where a more analytical person would more probably use the word "aspects". English is not a very exact language. If you want to express "exact" concepts, mathematics is a much more exact language: i.e., what is meant by an expression is usually much better defined than expressions in English.

Have fun -- Dick

 

[Doctordick]

Thank you for the vote of confidence Dr. D.

Thinking is not an easy thing to do. A lot of people value knowledge very highly because it relieves them of the need to think. I am afraid you are getting sufficiently long in the tooth that you would rather depend on what you "know" than think about it. If that is a false impression and you want me to change my opinion, you need to make some comments can be taken differently and not just quote academic catechism.

So what the heck do you mean? when you say:

Scientists avoid thinking about this issue by placing their reference clocks in specific reference frames as if these frames are of special significance.

They demand that dx, dy, and dz of the space-time lines of their clocks vanish in their reference frame! They make no such constraint on the character of their rulers. All they ask of their rulers is that (dx/dt +dy/dt +dz/dt) vanish for any specific measurement in that frame of reference (a subtly different issue). Of course, they don't expressly put that in their catechism as it might draw attention to this special treatment and open questions about the use of clocks as measuring devices.

Have fun -- Dick

 

[Antonio Lao]

Doctordick,

Time is relative. Spacetime is absolute. To me, any future consideration of using the derivative has to be rate of change of something with respect to spacetime. I really don't know how to do this, mathematically speaking. In other words, I don't understand when spacetime takes the value of zero. Is this the singularity? Where all physical variables are known to be infinite (density, energy, temperature). But the time, volume are all zero at the singularity. I know cosmologists, like Hawking and Penrose, refuse to talk about the naked singularity. They censor it.

 

[Doctordick]

Doctordick,

Time is relative. Spacetime is absolute. To me, any future consideration of using the derivative has to be rate of change of something with respect to spacetime. I really don't know how to do this, mathematically speaking. In other words, I don't understand when spacetime takes the value of zero. Is this the singularity? Where all physical variables are known to be infinite (density, energy, temperature). But the time, volume are all zero at the singularity. I know cosmologists, like Hawking and Penrose, refuse to talk about the naked singularity. They censor it.

Thank you very much for clarifying your position. I think I may have a better understanding of where you are coming from. When you say "spacetime is absolute", I suspect you are complaining about something I often complained about when I was a graduate student. I used to say that Einstein's representation of the universe was not dynamic but static and none of my professors seemed to comprehend what I was talking about.

I often bring up the issue of magicians and how they hide what they are doing through misdirection of attention because I think most professional scientists are guilty of the same ruse. (I only said that because people get tired of me saying it, especially if they don't understand why I say it.)

When I would say the relativistic picture was not dynamic they would point to the "time" axis and say "here is the dynamic component of the relativistic picture". But, when I said it was just a coordinate like any other coordinate in the representation and, in Einstein's picture, it is no more a source of change than is x or y, they would say "Oh, but it is quite different as, in Einstein's picture the geometry of the universe has quite a different metric and 'time' is quite different from 'space'; that is why it is called a space-time continuum!" And I would say, "Ah, yes; in Einstein's picture, time is imaginary!" Now there is a joke in there which no physicist I have ever met sees.

The issue of course is that there is no explicit parameter of change in Einstein's picture. That makes talking about how things change very difficult. Professional physicists handle the situation by moving from subject to subject to subject until the student gives up questioning the validity of their position and accepts their representation as free of difficulties. I call that procedure "misdirection of attention" and it is very effective at quelling investigative examination.

To me, any future consideration of using the derivative has to be rate of change of something with respect to spacetime. I really don't know how to do this, mathematically speaking.

That is because you really want to consider how things change with respect to time. In Einstein's picture, all things are space-time entities. In other words, you want to know how "space-time entities" change in time.

Now the physicists, being well trained in misdirection of attention will point out that all you want is the collection of space like cross sections of those space-time entities. If you then point out that, if one looks at space like cross sections of entities, they are no longer looking at space-time entities as the time coordinate has vanished, they will (driving home that spike of misdirection) point out that it is still a space-time entity which can be seen by transforming to a different frame of reference (and time will come right back into the description of the entity): i.e., it is as much of a space-time entity as it ever was.

When I was a first year graduate student I brought up that issue with one of the theoretical professors whom I held in high respect. I showed him the Euclidian representation of a correct relativistic space which I brought up on this thread (message #40). I showed him how it allowed a "dynamic" view of what was going on. He told me that, so long as it gave me the correct answers to problems there was nothing wrong with using the view but "please don't show it to the other students, it will just confuse them!" (By the way, he gave me the best grade in the class and, as far as I am aware, he held me as the best student he had.) I respected the man enough that I did not tell any of the other students about my observation.

Now in some respects, that advice could be seen as the worst possible advice he could have given me. On the other hand, it is also possible that I managed to get a Ph.D. in theoretical physics simply because I didn't try to fight the system until well after I graduated.

At any rate, I personally think you can trace your problem to the fact that the accepted picture of the universe supported by the current academy is just simply not convenient for analyzing the things you want to analyze. As a map maker, you should recognize the advantage of choosing the best coordinate system. (The Mercator projection is wrong but it sure serves its purpose so long as one remembers its shortcomings. In the same vein, I would hold that Einstein's space-time continuum is an invalid representation of reality but also provides very valuable service so long as one remembers its shortcomings.)

With regard to singularities, I am firmly of the opinion that a correct mental image of the universe should be totally without singularity. People forget that "infinity" is not a "number". "Infinity" is a tag attached to the description of a procedure allowing quick and easy reference to a special, rather common, circumstance in mathematics. Singularities arise when ever one attempts to push a mathematical representation of a problem beyond the applicability of the model behind that representation. It follows that any competent "physicist" wants you to switch models before you get there. Rus_Waters gave an answer to someone's question on this forum which was essentially a statement that what the person was talking about was not a quantum mechanical system. Compartmentalized thinking is much more conducive to misdirection of attention than is generalized conceptualization.

I say that any answer which is wrong in the limit of its definition is the wrong answer and professional physicists don't like that.

Sorry about my overly long answer!

Have fun -- Dick

 

[Antonio Lao]

Thanks for your overly long answer.

 

[PFanalog57]

Thinking is not an easy thing to do. A lot of people value knowledge very highly because it relieves them of the need to think. I am afraid you are getting sufficiently long in the tooth that you would rather depend on what you "know" than think about it.

Yes, you are correct. I am getting long in the tooth.


The key to "unification" is symmetry.



A timeless symmetry?

An infinite number of coin flips gives an equal amount of heads and an equal amount of tails.

[1/2 H and 1/2 T]*n, for n--->oo

A radioactive nucleus decays in accordance with probability P within time t_0 to time t_1

Probability P becomes a timeless mathematical entity governing the future iterations of events at time t. There exists a spectrum of possibilities for the observed quantities. Certain deterministic factors become contingent with respect to uncertainty, DxDp >= h .

An infinite number of observations of the radioactive decay, converges to an exact number for t?

Wave function probability density = |psi (r, t)|^2


The physical meaning of the expectation value is simple. It is the value that would be found by taking the average of many measurements of the observables in question on a large collection of systems all in the state psi. the individual results are weighted by the probability.

As Hawking says, the laws of physics must hold everywhere, including at the beginning of the universe. A triumph for the principles of democracy. Ergo, no singularity.

The one inch equation:

[<-[-><-]->]

The brackets, or parentheses, represent cotangent bundles. The arrows represent tangent vectors.

U stands for "universe", or, quantum particle. Energy conservation is time symmetric. This is a self similarity that holds for any aspect, or the "whole".

The "tau" parameter becomes a function of three coordinates on the surface of the embedded 3 dimensional manifold.

 

[Doctordick]

I have no idea what you are talking about!

And I see no connection between what you are saying and what I am trying to communicate. Sorry I am so dense.

Have fun -- Dick