If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

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Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

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RECENT POSTS IN THIS TOPIC

**Dr. Elliot McGucken**: *on* 3/3/17 at 20:28pm UTC, wrote Greetings Friends! Would love to send you free review copies of my new...

**Steve Clark**: *on* 3/15/10 at 5:12am UTC, wrote I'm sorry, I previously added this as a reply rather than a new post: ...

**Steve Clark**: *on* 3/15/10 at 4:42am UTC, wrote Dear Dr. E, In your attachment: :MOVING DIMENSIONS THEORY EXAMINES THE...

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FQXi FORUM

October 1, 2022

CATEGORY:
What's Ultimately Possible in Physics? Essay Contest (2009)
[back]

TOPIC: What is Ultimately Possible in Physics? Physics! A Hero’s Journey with Galileo, Newton, Faraday, Maxwell, Planck, Einstein, Schrodinger, Bohr, and the Greats towards Moving Dimensions Theory. E pur si muove! by Dr. Elliot McGucken [refresh]

TOPIC: What is Ultimately Possible in Physics? Physics! A Hero’s Journey with Galileo, Newton, Faraday, Maxwell, Planck, Einstein, Schrodinger, Bohr, and the Greats towards Moving Dimensions Theory. E pur si muove! by Dr. Elliot McGucken [refresh]

Over the past few decades prominent physicists have noted that physics has diverged away from its heroic journey defined by boldly describing, fathoming, and characterizing foundational truths of physical reality via simple, elegant, logically-consistent postulates and equations humbling themselves before empirical reality. Herein the spirit of physics is again exalted by the heroic words of the Greats—by Galileo, Newton, Faraday, Maxwell, Planck, Einstein, Bohr, and Schrodinger—the Founding Fathers upon whose shoulders physics stands. And from that pinnacle, a novel physical theory is proposed, complete with a novel physical model celebrating a hitherto unsung universal invariant and an equation reflecting the foundational physical reality of a fourth dimension expanding relative to the three spatial dimensions at the rate of c, or dx4/dt=ic, providing both the “elementary foundations” for relativity and QM’s “characteristic trait”—entanglement, and its nonlocal, probabilistic nature. From MDT’s experimentally-verified equation relativity is derived while time is unfrozen and free will exalted, while a physical model accounting for quantum nonlocality is presented. Entropy, Huygens’ Principle; the wave/particle, energy/mass, space/time, and E/B dualities; and time and all its arrows and asymmetries emerge from a common, foundational physical model. MDT exalts Einstein’s “empirical facts,” “naturalness,” and “logical simplicity.” For the first time in the history of relativity, change is woven into the fabric of space-time, and the timeless, ageless, nonlocal photon of Galileo’s/Einstein’s “empirical world” is explained via a foundational physical model, alongside the fact that c is both constant and the maximum velocity in the universe. The empirical GPS clocks’ time dilation/twins paradox is resolved by proposing a frame of absolute rest—the three spatial dimensions, and a frame of absolute motion—the fourth expanding dimension upon which ageless photons of zero rest mass surf; which underlie and give rise to Einstein’s Principle of Relativity.

“Dr. E” received a B.A. in physics from Princeton University and a Ph.D. in physics from UNC Chapel Hill, where his research on an artificial retina, which is now helping the blind see, appeared in NSF’s Frontiers and Popular Science and was awarded a Merrill Lynch Innovations Grant. While at Princeton, McGucken worked on projects concerning quantum mechanics and general relativity with the late John A. Wheeler, and the projects combined to form an appendix treating time as an emergent phenomenon in his dissertation. McGucken is writing a book artsentrepreneurship.com curriculum he created: The Gold 45 Revolver: The Hero’s Journey.

"The expansion of the fourth dimension is the source of nonlocality, entanglement, time and all its arrows and asymmetries, c, relativity, entropy, free will, and all motion, change, and measurement, for no measurement can be made without change."

Dr. Elliot McGucken,

Welcome to the second essay contest. Would you please expound on free will?

James Putnam

report post as inappropriate

Dr. Elliot McGucken,

Welcome to the second essay contest. Would you please expound on free will?

James Putnam

report post as inappropriate

Thanks for the words James,

Up until MDT, interpretations of relativity froze time and lay out the future before us in a pre-determined block universe.

All of relativity is derived from MDT's simple postulate and equation, which also provides for free will.

Free will means that the future does not yet exist, and we are free to influence it.

Best,

Dr. E

Up until MDT, interpretations of relativity froze time and lay out the future before us in a pre-determined block universe.

All of relativity is derived from MDT's simple postulate and equation, which also provides for free will.

Free will means that the future does not yet exist, and we are free to influence it.

Best,

Dr. E

Dr. Elliot McGucken,

I have thought about this question since the first contest but, was reluctant to ask it; because, it could be interpreted as confrontational instead of inquisitive. I have decided to give it a try. Whenever a theorist introduces a hidden, or at least unobservable by instrument, dimension, I feel that they are really saying something similar to "Don't pay any attention to the man behind the curtain." I don't question the theory in the sense of the things that it theoretically explains. I think if we add enough dimensions or additional 'filing cabinets', we can theoretically explain or 'store' everything away. What can convincingly be said about your theory that relies upon non-theoretical ideas? Maybe this question is too restricted. If you think so, I understand.

James

report post as inappropriate

I have thought about this question since the first contest but, was reluctant to ask it; because, it could be interpreted as confrontational instead of inquisitive. I have decided to give it a try. Whenever a theorist introduces a hidden, or at least unobservable by instrument, dimension, I feel that they are really saying something similar to "Don't pay any attention to the man behind the curtain." I don't question the theory in the sense of the things that it theoretically explains. I think if we add enough dimensions or additional 'filing cabinets', we can theoretically explain or 'store' everything away. What can convincingly be said about your theory that relies upon non-theoretical ideas? Maybe this question is too restricted. If you think so, I understand.

James

report post as inappropriate

Dr. Elliot McGucken,

A post script to my last message. I asked you this question instead of others because you have only one extra dimension. I wouldn't ask it of those who accept 8 or 10 or more extra hidden dimensions.

James

report post as inappropriate

A post script to my last message. I asked you this question instead of others because you have only one extra dimension. I wouldn't ask it of those who accept 8 or 10 or more extra hidden dimensions.

James

report post as inappropriate

Thanks James,

x4 is as physically real as x1, x2, and x3.

x4 pervades relativity theory, which has never been proven false in countless physical experiments, and which has successfully predicted countless physical observables.

x4 is both mathematically useful and physically real.

Please check out any of Einstein's books on Relativity, and you will see it there.

Hope this helps.

Best,

Dr. E

x4 is as physically real as x1, x2, and x3.

x4 pervades relativity theory, which has never been proven false in countless physical experiments, and which has successfully predicted countless physical observables.

x4 is both mathematically useful and physically real.

Please check out any of Einstein's books on Relativity, and you will see it there.

Hope this helps.

Best,

Dr. E

Dr. Elliot McGucken,

Since my very first introduction to the theory of relativity, I have had an intrinsic reluctance to believe it. Using it as a workable theory is ok. I have 'The Meaning of Relativity' by Albert Einstein. I will try re-reading that one with an open mind. However, I can already feel that reluctance coming over me again. Thank you for your answer.

James

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Since my very first introduction to the theory of relativity, I have had an intrinsic reluctance to believe it. Using it as a workable theory is ok. I have 'The Meaning of Relativity' by Albert Einstein. I will try re-reading that one with an open mind. However, I can already feel that reluctance coming over me again. Thank you for your answer.

James

report post as inappropriate

Dr. Elliot McGucken,

With due respect for the talents of both you and Dr. Crowell; just in case you haven't noticed:

CATEGORY: Blog

TOPIC: Vita Nuova

"Lawrence B. Crowell wrote on Sep. 18, 2009 @ 00:42 GMT

That is probably the case. In fact due to expense and other matters NASA can't get the US manned space program out of Earth orbit. The speed of light is an invariant. I am not a strong exponent of McGucken's idea of moving dimensions, he has a paper on the essay page, but he keeps making a point that along the 4th dimension we move at x_4 = ct, or the speed of light. So everything in a way is moving the speed of light, no faster or slower. This is a rather elementary fact of special relativity, but it makes a point of this ultimate invariant of the speed of light.

Jump drives or wormholes suffer from the same problem as with warp drives, the energy required as the source of the spacetime configuration is negative. These things likely to be appear ruled out.

We are most not only stuck to speeds slower than light, but probably we are simply stuck here on Earth. Space is interesting to study and send probes or instruments into, but I doubt we are really going to live there

Cheers LC"

James

report post as inappropriate

With due respect for the talents of both you and Dr. Crowell; just in case you haven't noticed:

CATEGORY: Blog

TOPIC: Vita Nuova

"Lawrence B. Crowell wrote on Sep. 18, 2009 @ 00:42 GMT

That is probably the case. In fact due to expense and other matters NASA can't get the US manned space program out of Earth orbit. The speed of light is an invariant. I am not a strong exponent of McGucken's idea of moving dimensions, he has a paper on the essay page, but he keeps making a point that along the 4th dimension we move at x_4 = ct, or the speed of light. So everything in a way is moving the speed of light, no faster or slower. This is a rather elementary fact of special relativity, but it makes a point of this ultimate invariant of the speed of light.

Jump drives or wormholes suffer from the same problem as with warp drives, the energy required as the source of the spacetime configuration is negative. These things likely to be appear ruled out.

We are most not only stuck to speeds slower than light, but probably we are simply stuck here on Earth. Space is interesting to study and send probes or instruments into, but I doubt we are really going to live there

Cheers LC"

James

report post as inappropriate

Thanks James,

The one and only velocity through space-time is c.

When matter is caught in the fourth expanding dimension, it moves at c relative to the three spatial dimensions and appears as photons. When matter is stationary in our lab, it is mostly propagating at c relative to the fourth dimension, which is only because the fourth dimension is expanding at the rate of c relative...

view entire post

The one and only velocity through space-time is c.

When matter is caught in the fourth expanding dimension, it moves at c relative to the three spatial dimensions and appears as photons. When matter is stationary in our lab, it is mostly propagating at c relative to the fourth dimension, which is only because the fourth dimension is expanding at the rate of c relative...

view entire post

Welcome back to the contests Dr. E.

I have seen and read your MDT here and elsewhere and I think I grasp the idea. Now I would like to see less marketing and some more formulas and predictions, maybe doable experiment to test it or at least probe it wrong.

Forgive me if I am rude, but it almost allways comes with a quicker answer.

Best...

Juan

report post as inappropriate

I have seen and read your MDT here and elsewhere and I think I grasp the idea. Now I would like to see less marketing and some more formulas and predictions, maybe doable experiment to test it or at least probe it wrong.

Forgive me if I am rude, but it almost allways comes with a quicker answer.

Best...

Juan

report post as inappropriate

Thanks Juan,

Firstoff, do you agree with these simple proofs of MDT?

"Simple, logical proofs of MDT:

MDT PROOF#1: Relativity tells us that a timeless, ageless photon remains in one place in the fourth dimension. Quantum mechanics tells us that a photon propagates as a spherically-

3

symmetric expanding wavefront at the velocity of c. Ergo, the fourth dimension...

view entire post

Firstoff, do you agree with these simple proofs of MDT?

"Simple, logical proofs of MDT:

MDT PROOF#1: Relativity tells us that a timeless, ageless photon remains in one place in the fourth dimension. Quantum mechanics tells us that a photon propagates as a spherically-

3

symmetric expanding wavefront at the velocity of c. Ergo, the fourth dimension...

view entire post

Thanks for the response Dr E

Now a new question.

I understand MDT is derived from relativity so the experiments to test relativity work for MDT. Also block universe is derived from relativity. Why would we think MDT is the right one? Is there a test to differentiate MDT from block time apart from the perception of free will and the arrow of time?

report post as inappropriate

Now a new question.

I understand MDT is derived from relativity so the experiments to test relativity work for MDT. Also block universe is derived from relativity. Why would we think MDT is the right one? Is there a test to differentiate MDT from block time apart from the perception of free will and the arrow of time?

report post as inappropriate

Thanks Juan,

No--all of relativity is derived form MDT's simple postulate and equation:

The fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt=ic.

Give me a universe with x1, x2, x3, x4 and wherein dx4/dt=ic and all of relativity naturally arises, including Einstein's Principle of Relativity and his two postualtes.

Relativity is derived...

view entire post

No--all of relativity is derived form MDT's simple postulate and equation:

The fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt=ic.

Give me a universe with x1, x2, x3, x4 and wherein dx4/dt=ic and all of relativity naturally arises, including Einstein's Principle of Relativity and his two postualtes.

Relativity is derived...

view entire post

p.s. MDT is more fundamental than relativity and it also grants us entropy and QM's characteristic trait--entanglement.

An added benefit are all the other entities dx4/dt=ic accounts for with a physical model, ranging from entropy, to QM's entanglement and nonlocality, to time and all its arrows. MDT accomplishes a diverse array of physical feats:

∗provides the “elementary...

view entire post

An added benefit are all the other entities dx4/dt=ic accounts for with a physical model, ranging from entropy, to QM's entanglement and nonlocality, to time and all its arrows. MDT accomplishes a diverse array of physical feats:

∗provides the “elementary...

view entire post

Dr E

You are quick at writing, let me take a new look to your writings around the net, but don't worry I'll be back.

Best...

Juan Ramos

report post as inappropriate

You are quick at writing, let me take a new look to your writings around the net, but don't worry I'll be back.

Best...

Juan Ramos

report post as inappropriate

Hello Dr. Elliot McGucken,

At the beginning ,when I found FQXi ,I was surprised by your Theory about the relativity .

I understand better now your extrapolations .

I think what it's rather a special relativity .

I liked read your essay ,it's relevant but I don't think really it's better than our fundamenatl general relativity .It's a little strong that no???

And the spherical gravitational waves thus ????

In all case ,congratulations for your development .Very creative .

Sincerely

Steve

report post as inappropriate

At the beginning ,when I found FQXi ,I was surprised by your Theory about the relativity .

I understand better now your extrapolations .

I think what it's rather a special relativity .

I liked read your essay ,it's relevant but I don't think really it's better than our fundamenatl general relativity .It's a little strong that no???

And the spherical gravitational waves thus ????

In all case ,congratulations for your development .Very creative .

Sincerely

Steve

report post as inappropriate

Thanks Steve!

MDT underlies both special relativity and general relativity. From its simple postulate and equation, both special and general relativity can be derived.

Einstein always stated that relativity needed a more fundamental formulation--a foundational precept from where it all arises. Well, here it is:

The fourth dimension is expanding relative to teh trhee spatial dimensions at c. dx4/dt=ic.

And too, we gain a physical model for all of entropy and QM's characteristic trait--entanglement and nonlocality.

attachments: 3_2_MDT_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf, 1_2_wheeler_recommendation_mcgucken_medium.jpg

MDT underlies both special relativity and general relativity. From its simple postulate and equation, both special and general relativity can be derived.

Einstein always stated that relativity needed a more fundamental formulation--a foundational precept from where it all arises. Well, here it is:

The fourth dimension is expanding relative to teh trhee spatial dimensions at c. dx4/dt=ic.

And too, we gain a physical model for all of entropy and QM's characteristic trait--entanglement and nonlocality.

attachments: 3_2_MDT_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf, 1_2_wheeler_recommendation_mcgucken_medium.jpg

p.s. in the above attachments, please find some elaborations on MDT in the context of GR.

Best & thanks for your time & feedback,

Elliot

Best & thanks for your time & feedback,

Elliot

Dear Dr. Elliot McGucken,

Formulation of a set of dualities to construct a probabilistic universe by MDT may emerge with a deterministic universe and in a Coherent-cyclic cluster-matter universe model the energy/mass is expressed as function, where the analogy of speed of light is not constant as this energy-mass function propagates in matrix by a cyclic transfer phenomena as waves and the speed of propagation depends on the rotation of matrix elements that conduct energy-mass.

As per this model, the space/time duality described in MDT is the space-time tensor field that is a function and the wave/particle duality is substituted by the wave propagation action path in a matrix.

Though the entanglement of photons described in MDT is not applicable for this model, the MDT itself is applicable with different perspectives on this model as the tensor field is the particle/matter. Happy to say, thank you ..

With best wishes,

Jayakar

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Formulation of a set of dualities to construct a probabilistic universe by MDT may emerge with a deterministic universe and in a Coherent-cyclic cluster-matter universe model the energy/mass is expressed as function, where the analogy of speed of light is not constant as this energy-mass function propagates in matrix by a cyclic transfer phenomena as waves and the speed of propagation depends on the rotation of matrix elements that conduct energy-mass.

As per this model, the space/time duality described in MDT is the space-time tensor field that is a function and the wave/particle duality is substituted by the wave propagation action path in a matrix.

Though the entanglement of photons described in MDT is not applicable for this model, the MDT itself is applicable with different perspectives on this model as the tensor field is the particle/matter. Happy to say, thank you ..

With best wishes,

Jayakar

report post as inappropriate

Thanks Jayakar,

The beauty of MDT is that it offers a *physical* model underlying QM and relativity and a *physical* theory, actually proposing a new fundamental *physical* invariant--that of a fourth expanding dimension which expands at c.

And all of a sudden, we have a *physical* model and *physical* reasons for entanglement, entropy, and relativity.

MDT is more fundamental...

view entire post

The beauty of MDT is that it offers a *physical* model underlying QM and relativity and a *physical* theory, actually proposing a new fundamental *physical* invariant--that of a fourth expanding dimension which expands at c.

And all of a sudden, we have a *physical* model and *physical* reasons for entanglement, entropy, and relativity.

MDT is more fundamental...

view entire post

Many of you would also enjoy my essay from last year, wherein relativity is derived form MDT's simple postulate and equation:

http://fqxi.org/community/forum/topic/238

TOPIC: Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken

Essay Abstract

In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth...

view entire post

http://fqxi.org/community/forum/topic/238

TOPIC: Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken

Essay Abstract

In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth...

view entire post

Hi Eliot ,

You are welcome .And thanks too for the attachements .

I am going to read it .

Sincerely

best regards

Steve

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You are welcome .And thanks too for the attachements .

I am going to read it .

Sincerely

best regards

Steve

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Hi Dear Elliot ,

It's very interesting .

I have seen the wheeler writing ,it's interesting about the EPR paradox .

I don't know well ,could explain me a little theses intrications and hideen variables .

The Copenhagen Interpretation and the EPR paradox ??could you resume this two extrapolated thoughts .

If I understand well, one is pragmatic,utilise tools to predict the quantum mechanic and the other uses hidden variables or others hidden parameters .

What is this cyclotron too ?

I am going to see...

Best Regards

Steve

report post as inappropriate

It's very interesting .

I have seen the wheeler writing ,it's interesting about the EPR paradox .

I don't know well ,could explain me a little theses intrications and hideen variables .

The Copenhagen Interpretation and the EPR paradox ??could you resume this two extrapolated thoughts .

If I understand well, one is pragmatic,utilise tools to predict the quantum mechanic and the other uses hidden variables or others hidden parameters .

What is this cyclotron too ?

I am going to see...

Best Regards

Steve

report post as inappropriate

Thanks Steve

All experiments and major theories point not towards hidden variables, but entanglement.

As MDT embraces all experiments and major theories--both relativity and quantum mechanics--it embraces entanglement.

Best,

Dr. E :)

All experiments and major theories point not towards hidden variables, but entanglement.

As MDT embraces all experiments and major theories--both relativity and quantum mechanics--it embraces entanglement.

Best,

Dr. E :)

I agree ,Rational indeed ,an entanglement ,predicted with fundamentals, will give the best results .

The number of entangled spheres is specific I think like an universal link between spheres .

And furtheremore possesses others properties like the volumes ,the velocities of rot ,the senses ,the directions ,the angles .Thus the lattices too are specifics .

Sometimes ,I imagine...

view entire post

The number of entangled spheres is specific I think like an universal link between spheres .

And furtheremore possesses others properties like the volumes ,the velocities of rot ,the senses ,the directions ,the angles .Thus the lattices too are specifics .

Sometimes ,I imagine...

view entire post

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Dear Dr. Elliot McGucken

Yes fourth coordinate dx4 = ic x dt

is a coordinate of motion.

And this coordinate is not time.

In the formula symbol t is the number that represent "tick" of clock that measures certain motion.

Clocks run in timeless quantum space.

yours amrit

attachments: 4_MATHEMATICAL_SPACETIME__NEURONAL_SPACETIME_AND_TIMELESS_QUANTUM_SPACE_arXiv.doc

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Yes fourth coordinate dx4 = ic x dt

is a coordinate of motion.

And this coordinate is not time.

In the formula symbol t is the number that represent "tick" of clock that measures certain motion.

Clocks run in timeless quantum space.

yours amrit

attachments: 4_MATHEMATICAL_SPACETIME__NEURONAL_SPACETIME_AND_TIMELESS_QUANTUM_SPACE_arXiv.doc

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Dear Dr. Elliot McGucken

You Say: For the first time in the history of relativity, change is woven into the fabric of space-time, and the timeless, ageless, nonlocal photon of Galileo’s/Einstein’s “empirical world” is explained via a foundational physical model, alongside the fact that c is both constant and the maximum velocity in the universe. The empirical GPS clocks’ time dilation/twins paradox is resolved by proposing a frame of absolute rest—the three spatial dimensions, and a frame of absolute motion—the fourth expanding dimension upon which ageless photons of zero rest mass surf; which underlie and give rise to Einstein’s Principle of Relativity.

What you say above simply means that quantum space is timeless and that physical time is run of clocks. In Einsten Relativity is relative velocity of clocks and velovity of all material change. That 4-th coordinate of space-time is spatial too was discussing already Godel. See my article on vixra: Experimental Proof for Godel Theorem on Time

http://vixra.org/pdf/0910.0041v1.pdf

yours amrit

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You Say: For the first time in the history of relativity, change is woven into the fabric of space-time, and the timeless, ageless, nonlocal photon of Galileo’s/Einstein’s “empirical world” is explained via a foundational physical model, alongside the fact that c is both constant and the maximum velocity in the universe. The empirical GPS clocks’ time dilation/twins paradox is resolved by proposing a frame of absolute rest—the three spatial dimensions, and a frame of absolute motion—the fourth expanding dimension upon which ageless photons of zero rest mass surf; which underlie and give rise to Einstein’s Principle of Relativity.

What you say above simply means that quantum space is timeless and that physical time is run of clocks. In Einsten Relativity is relative velocity of clocks and velovity of all material change. That 4-th coordinate of space-time is spatial too was discussing already Godel. See my article on vixra: Experimental Proof for Godel Theorem on Time

http://vixra.org/pdf/0910.0041v1.pdf

yours amrit

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dx4/dt = ic

If this formula is correct than Planck distance dP devided with Plank time tP

most be light speed

dP/tP = ic

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If this formula is correct than Planck distance dP devided with Plank time tP

most be light speed

dP/tP = ic

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I like your thinking. I was first stuck by the basic intuitive sense MDT makes

in your Time contest essay. You say it provides a "foundational physical reality"

for time, so I wonder about that 'metaphysical' elephant just outside the room...

into what is your expanding sphere of time expanding?

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in your Time contest essay. You say it provides a "foundational physical reality"

for time, so I wonder about that 'metaphysical' elephant just outside the room...

into what is your expanding sphere of time expanding?

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Thanks Amrit,

What is the "Godel Theorem on Time?" Where can I read more on what Godel thought?

Thanks!

Dr. E

What is the "Godel Theorem on Time?" Where can I read more on what Godel thought?

Thanks!

Dr. E

Thanks TR,

Time is not the fourth dimension.

The fourth dimenion is just like the three spatial dimensions, except that it is moving at c relative to the three spatial dimensions.

When we draw a time axis on the standard x-t graph, the time axis is a human construct, as only in our minds do the past and future exist. Time--the ticking of seconds on our watches--emerges from the fact that teh fourth dimension is expanding relative to the three spatial dimensions at c.

Simple proofs of MDT:

PROOF#1:

Relativity tells us that a timeless, ageless photon remains in one place in the fourth dimension.

Quantum mechanics tells us that a photon propagates as a spherically-symmetric expanding wavefront at the velocity of c.

Ergo, the fourth dimension must be expanding relative to the three spatial dimensions at the rate of c, in a spherically-symmetric manner.

The expansion of the fourth dimension is the source of nonlocality, time and all its arrows and asymmetries, c, relativity, entropy, free will, and all motion, change, and measurement, for no measurement can be made without change.

For the first time in the history of relativity, change has been wedded to the fundamental fabric of spacetime in MDT.

PROOF#2:

Einstein and Minkowski wrote x4=ict

Ergo dx4/dt=ic.

PROOF#3:

The only way to stay stationary in the three spatial dimensions is to move at c through the fourth dimension. The only way to stay stationary in the fourth dimension is to move at c through the three spatial dimensions. Ergo the fourth dimension is moving at c relative to the three spatial dimensions.

http://www.facebook.com/topic.php?uid=2204722738&

topic=37923

attachments: ja_wheeler_recommendation_mcgucken2.jpg, dissertation.jpg

Time is not the fourth dimension.

The fourth dimenion is just like the three spatial dimensions, except that it is moving at c relative to the three spatial dimensions.

When we draw a time axis on the standard x-t graph, the time axis is a human construct, as only in our minds do the past and future exist. Time--the ticking of seconds on our watches--emerges from the fact that teh fourth dimension is expanding relative to the three spatial dimensions at c.

Simple proofs of MDT:

PROOF#1:

Relativity tells us that a timeless, ageless photon remains in one place in the fourth dimension.

Quantum mechanics tells us that a photon propagates as a spherically-symmetric expanding wavefront at the velocity of c.

Ergo, the fourth dimension must be expanding relative to the three spatial dimensions at the rate of c, in a spherically-symmetric manner.

The expansion of the fourth dimension is the source of nonlocality, time and all its arrows and asymmetries, c, relativity, entropy, free will, and all motion, change, and measurement, for no measurement can be made without change.

For the first time in the history of relativity, change has been wedded to the fundamental fabric of spacetime in MDT.

PROOF#2:

Einstein and Minkowski wrote x4=ict

Ergo dx4/dt=ic.

PROOF#3:

The only way to stay stationary in the three spatial dimensions is to move at c through the fourth dimension. The only way to stay stationary in the fourth dimension is to move at c through the three spatial dimensions. Ergo the fourth dimension is moving at c relative to the three spatial dimensions.

http://www.facebook.com/topic.php?uid=2204722738&

topic=37923

attachments: ja_wheeler_recommendation_mcgucken2.jpg, dissertation.jpg

Thanks Dr.E, again, a "spherically-symmetic expansion" is a contextual expression, I'm wondering if you have given any thought as to what all these

expanding photons are 'expanding into'? Also, do you ascribe any attributes

to this moving dimension of time other than it is spherically expanding a c?

In other words, what IS it?

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expanding photons are 'expanding into'? Also, do you ascribe any attributes

to this moving dimension of time other than it is spherically expanding a c?

In other words, what IS it?

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Thanks TR,

Well, it is the exact same thing as the three spatial dimensions, but for the fact that it is expanding at c relative to them.

In General Relativity the dimensions bend, warp, and move (whatever they might be!)

And in order for a dimension to bend, warp, or move, it must be bending, warping or moving relative to something in GR. :)

So really, MDT is not all that new, other than its stipulation that the fourth dimension is expanding relatyive to the three spatial dimensions or dx4/dt=ic, which all of a sudden gives rise to relativity as well as entorpy and quantum entanglement.

Well, it is the exact same thing as the three spatial dimensions, but for the fact that it is expanding at c relative to them.

In General Relativity the dimensions bend, warp, and move (whatever they might be!)

And in order for a dimension to bend, warp, or move, it must be bending, warping or moving relative to something in GR. :)

So really, MDT is not all that new, other than its stipulation that the fourth dimension is expanding relatyive to the three spatial dimensions or dx4/dt=ic, which all of a sudden gives rise to relativity as well as entorpy and quantum entanglement.

Thanks again E, I know physics isn't concerned with metaphysics - ontology and epistemology, it's about the mathematics behind the 'mechanics', so thanks for extending an answer anyway. I noticed that the word gravity appears no where in your essays, where does this "mysterious action at a distance" fit into your way of thinking? Are you more of the classical curvature school or tending toward quantum string unification theory.

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Hello!

Attached please find how MDT accounts for the gravitational redshift!

As space is stretched by mass and the fourth dimension's expansion remains constant, an object naturally moves towards the mass and into the stretched spatial dimensions so as to keep the space/time ration constant--so as to move in straight line through space-time.

Enjoy!

Best,

Dr. E :)

attachments: 1_6_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf, 1_1_2_wheeler_recommendation_mcgucken_medium.jpg

Attached please find how MDT accounts for the gravitational redshift!

As space is stretched by mass and the fourth dimension's expansion remains constant, an object naturally moves towards the mass and into the stretched spatial dimensions so as to keep the space/time ration constant--so as to move in straight line through space-time.

Enjoy!

Best,

Dr. E :)

attachments: 1_6_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf, 1_1_2_wheeler_recommendation_mcgucken_medium.jpg

Interesting, thanks E. You are aware I'm sure that in a DeSitter universe with matter sufficiently dispersed the apparent accelerated wavelength redshifting of distant cosmic objects is due not to their recession velocity but rather to frequency dilation related to the expansion of time, meaning that the universe isn't expanding ever faster in space - it's slowly running out of time. I know it's not a concern for physics but I'm still wondering what your expanding time is expanding into. I wonder if there is a more comprehensive dynamic driving time.

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I'm also wondering about the Planck scale quantization of time. The estimated value for the speed of light: 299,792,458... (and the gravitational constant for that matter: 6.67428...) while forever indeterminate beyond empirical magins of error, certainly appear to be, and may well be, irrational numbers. Such values remain indeterminate (in ever defining refinement) not because of experimental limatation but because they ARE continuous - part and parcel of a continuum and therefore not subject to quantization. Einstein: "I consider it quite possible that physics cannot be based on the field concept, that is on continuous structures. Then nothing remains of my entire castle in the air, including the theory of gravitation, but also nothing of the rest of modern physics." How can MDT be a derivation of the Einstein field metric while employing the concept of quantized time?

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Thanks TR! I am trying to keep MDT focused on its simple beauty at the moment. :)

Can anyone find any faults in these proofs of MDT?

Simple proofs of MDT:

PROOF#1:

Relativity tells us that a timeless, ageless photon remains in one place in the fourth dimension.

Quantum mechanics tells us that a photon propagates as a spherically-symmetric expanding wavefront at the velocity of c.

Ergo, the fourth dimension must be expanding relative to the three spatial dimensions at the rate of c, in a spherically-symmetric manner.

The expansion of the fourth dimension is the source of nonlocality, time and all its arrows and asymmetries, c, relativity, entropy, free will, and all motion, change, and measurement, for no measurement can be made without change.

For the first time in the history of relativity, change has been wedded to the fundamental fabric of spacetime in MDT.

PROOF#2:

Einstein and Minkowski wrote x4=ict

Ergo dx4/dt=ic.

PROOF#3:

The only way to stay stationary in the three spatial dimensions is to move at c through the fourth dimension. The only way to stay stationary in the fourth dimension is to move at c through the three spatial dimensions. Ergo the fourth dimension is moving at c relative to the three spatial dimensions.

http://www.facebook.com/topic.php?uid=2204722738&

topic=37923

Twitter proof:

SR: photon is stationary in 4th dimension. QM: photon is probability wave expanding @ c. Ergo: 4th dimension expands @ c. x4=ict-> dx4/dt=ic

http://twitter.com/45surf

Can anyone find any faults in these proofs of MDT?

Simple proofs of MDT:

PROOF#1:

Relativity tells us that a timeless, ageless photon remains in one place in the fourth dimension.

Quantum mechanics tells us that a photon propagates as a spherically-symmetric expanding wavefront at the velocity of c.

Ergo, the fourth dimension must be expanding relative to the three spatial dimensions at the rate of c, in a spherically-symmetric manner.

The expansion of the fourth dimension is the source of nonlocality, time and all its arrows and asymmetries, c, relativity, entropy, free will, and all motion, change, and measurement, for no measurement can be made without change.

For the first time in the history of relativity, change has been wedded to the fundamental fabric of spacetime in MDT.

PROOF#2:

Einstein and Minkowski wrote x4=ict

Ergo dx4/dt=ic.

PROOF#3:

The only way to stay stationary in the three spatial dimensions is to move at c through the fourth dimension. The only way to stay stationary in the fourth dimension is to move at c through the three spatial dimensions. Ergo the fourth dimension is moving at c relative to the three spatial dimensions.

http://www.facebook.com/topic.php?uid=2204722738&

topic=37923

Twitter proof:

SR: photon is stationary in 4th dimension. QM: photon is probability wave expanding @ c. Ergo: 4th dimension expands @ c. x4=ict-> dx4/dt=ic

http://twitter.com/45surf

I find another possibility arising from proofs 1 & 2... theoretical simultaneity at c occurs because the 3-D universe is expanding everywhere at ONCE, at the speed of light, INTO a 4th dimension of imaginary time (ic). This expansion would emerge from deep within, at the Planck scale - the domain of the 'wavefunction' - where according to QED everything generated is initially photonic, and therefore, simultaneous. One universe expanding at the same invariant velocity, everywhere at once. Photons appear to remain in one place because they ARE in one place - an endless emergent Present, the 3-D universe expanding in 4-D time.

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Thanks TR,

But does your theory explain nonlocality, entanglement, Hyuygens' principle, and entropy. Can you derive all of relativity from your thory?

It seems MDT is simpler than your tehory, while also having far more ranging consequences in the realm of explanations for physical phenomena.

Can anyone find any faults in these proofs of MDT?

Simple proofs of MDT:

PROOF#1:

Relativity tells us that a timeless, ageless photon remains in one place in the fourth dimension.

Quantum mechanics tells us that a photon propagates as a spherically-symmetric expanding wavefront at the velocity of c.

Ergo, the fourth dimension must be expanding relative to the three spatial dimensions at the rate of c, in a spherically-symmetric manner.

The expansion of the fourth dimension is the source of nonlocality, time and all its arrows and asymmetries, c, relativity, entropy, free will, and all motion, change, and measurement, for no measurement can be made without change.

For the first time in the history of relativity, change has been wedded to the fundamental fabric of spacetime in MDT.

PROOF#2:

Einstein and Minkowski wrote x4=ict

Ergo dx4/dt=ic.

PROOF#3:

The only way to stay stationary in the three spatial dimensions is to move at c through the fourth dimension. The only way to stay stationary in the fourth dimension is to move at c through the three spatial dimensions. Ergo the fourth dimension is moving at c relative to the three spatial dimensions.

http://www.facebook.com/topic.php?uid=2204722738&

topic=37923

Twitter proof:

SR: photon is stationary in 4th dimension. QM: photon is probability wave expanding @ c. Ergo: 4th dimension expands @ c. x4=ict-> dx4/dt=ic

http://twitter.com/45surf

But does your theory explain nonlocality, entanglement, Hyuygens' principle, and entropy. Can you derive all of relativity from your thory?

It seems MDT is simpler than your tehory, while also having far more ranging consequences in the realm of explanations for physical phenomena.

Can anyone find any faults in these proofs of MDT?

Simple proofs of MDT:

PROOF#1:

Relativity tells us that a timeless, ageless photon remains in one place in the fourth dimension.

Quantum mechanics tells us that a photon propagates as a spherically-symmetric expanding wavefront at the velocity of c.

Ergo, the fourth dimension must be expanding relative to the three spatial dimensions at the rate of c, in a spherically-symmetric manner.

The expansion of the fourth dimension is the source of nonlocality, time and all its arrows and asymmetries, c, relativity, entropy, free will, and all motion, change, and measurement, for no measurement can be made without change.

For the first time in the history of relativity, change has been wedded to the fundamental fabric of spacetime in MDT.

PROOF#2:

Einstein and Minkowski wrote x4=ict

Ergo dx4/dt=ic.

PROOF#3:

The only way to stay stationary in the three spatial dimensions is to move at c through the fourth dimension. The only way to stay stationary in the fourth dimension is to move at c through the three spatial dimensions. Ergo the fourth dimension is moving at c relative to the three spatial dimensions.

http://www.facebook.com/topic.php?uid=2204722738&

topic=37923

Twitter proof:

SR: photon is stationary in 4th dimension. QM: photon is probability wave expanding @ c. Ergo: 4th dimension expands @ c. x4=ict-> dx4/dt=ic

http://twitter.com/45surf

Well, we'll see. The TCH (Temporal Continuum Hypothesis) may also explain "dark matter" and "dark energy" and place the gravitational field in a comprehensive context that is both inclusive and exclusive of quantum dynamics... SingularityShuttle.com

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Please see attached paper!

“More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. . . .” –John Archibald Wheeler, Princeton University

On Deriving Relativity & Entanglement from MDT’s Fundamental Physical Reality: dx4/dt=ic

What is Ultimately Possible in Physics? Physics! A Hero’s...

view entire post

“More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. . . .” –John Archibald Wheeler, Princeton University

On Deriving Relativity & Entanglement from MDT’s Fundamental Physical Reality: dx4/dt=ic

What is Ultimately Possible in Physics? Physics! A Hero’s...

view entire post

attachments: 2_1_2_wheeler_recommendation_mcgucken_medium.jpg

oops--it seems the paper did not attach--let's try again!

attachments: On_Deriving_Relativity_Entanglement_from_MDTs_Fundamental_Physical_Reality_small.pdf

attachments: On_Deriving_Relativity_Entanglement_from_MDTs_Fundamental_Physical_Reality_small.pdf

Hi Dr E.

After an admittedly quickish read through your essay & some of the attached material, I must say I like the simplicity & potential for explanatory power of your theory. I do have one or two perhaps naive questions though.

Firstly, could you clarify whether or not the MDT 4th dimension is radiation only? ie consisting entirely of null surfaces, or does matter propagate there other than as photons?

Secondly, the invariant planck wavelength of the radiation manifested by the expansion would seem to imply that wavelength/energy is purely *locally* determined relative to the Lorentz signature of *local* space, independant of the wavelength when emitted from a source or prior to entering a gravitational field? Doesn't this conflict with the "observed" cosmic (3D) expansion red shift & the CMB for example? This also seems to imply that a photon moving toward a centre of mass would gain energy which, correct me if I'm wrong, is not normally observed?

Finally, a question on energy conservation. As energy is always observed to be conserved *within 3D space*, could you clarify how in MDT the "lost" energy of red shift & the "gained" energy of blue shift is accounted for *within 3D space* ?

Thanks for the thought provoking essay!

Cheers

Roy

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After an admittedly quickish read through your essay & some of the attached material, I must say I like the simplicity & potential for explanatory power of your theory. I do have one or two perhaps naive questions though.

Firstly, could you clarify whether or not the MDT 4th dimension is radiation only? ie consisting entirely of null surfaces, or does matter propagate there other than as photons?

Secondly, the invariant planck wavelength of the radiation manifested by the expansion would seem to imply that wavelength/energy is purely *locally* determined relative to the Lorentz signature of *local* space, independant of the wavelength when emitted from a source or prior to entering a gravitational field? Doesn't this conflict with the "observed" cosmic (3D) expansion red shift & the CMB for example? This also seems to imply that a photon moving toward a centre of mass would gain energy which, correct me if I'm wrong, is not normally observed?

Finally, a question on energy conservation. As energy is always observed to be conserved *within 3D space*, could you clarify how in MDT the "lost" energy of red shift & the "gained" energy of blue shift is accounted for *within 3D space* ?

Thanks for the thought provoking essay!

Cheers

Roy

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Thanks Roy!

You ask, "Firstly, could you clarify whether or not the MDT 4th dimension is radiation only? ie consisting entirely of null surfaces, or does matter propagate there other than as photons?"

A photon has zero rest mass. Ergo none of the photon is at rest.

And again, this supports MDT's fundamental tenet and offers yet another proof of a fourth expanding dimension: dx4/dt=ic. To move at the velocity of light means to exist in a state of absolute motion. And again, the fourth dimension defines absolute motion as it is propagating at the velocity of light, while teh three psatial dimensions define rest.

In MDT the three spatial dimensions define a state of rest, while the fourth expanding dimension defines absolute motion at c. Ergo zero rest mass implies zero rest, which implies that the photon exists entirely in the fourth dimension. Any time matter is caught in the fourth dimension, it appears as energy and moves with the veloicty c. Hence E=mc^2!

Now it is interesting that in order for an object to gain velocity, it must have energy added to it. And this adds to the object's mass, while also making it appear shorter in the three spatial dimensions (length contraction). Now that energy would exist entirely in the fourth dimension, and as the object gained more and more mass in teh fourth dimension, it would have a greater and greater probability of existing in the fourth dimension, and thus moving.

I would guess that only objects of zero rest mass can appear in the 4th dimension, as only then can all their mass be in the moving dimension. Any rest mass would imply that part of the object has a probability of being at rest in the three spatial dimensions.

Your second question is: "Secondly, the invariant planck wavelength of the radiation manifested by the expansion would seem to imply that wavelength/energy is purely *locally* determined relative to the Lorentz signature of *local* space, independant of the wavelength when emitted from a source or prior to entering a gravitational field? Doesn't this conflict with the "observed" cosmic (3D) expansion red shift & the CMB for example? This also seems to imply that a photon moving toward a centre of mass would gain energy which, correct me if I'm wrong, is not normally observed?"

The redhsift happens because as a photon moves away from a massive object, the space becomes less and less stretched, and the photon's wavelength appears longer and longer, as shown in the attached diagram; as the expansion of the fourth dimension is a constant, unaffected by gravity. The result of the constancy of dx4/dt=ic combined with the stretching of space results in time moving slower closer to massive objects, as illustrated in the figure.

And yes, when photons approach massive objects, they are blue-shifted! They gain energy!

attachments: 2_6_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf, 5_1_2_wheeler_recommendation_mcgucken_medium.jpg

You ask, "Firstly, could you clarify whether or not the MDT 4th dimension is radiation only? ie consisting entirely of null surfaces, or does matter propagate there other than as photons?"

A photon has zero rest mass. Ergo none of the photon is at rest.

And again, this supports MDT's fundamental tenet and offers yet another proof of a fourth expanding dimension: dx4/dt=ic. To move at the velocity of light means to exist in a state of absolute motion. And again, the fourth dimension defines absolute motion as it is propagating at the velocity of light, while teh three psatial dimensions define rest.

In MDT the three spatial dimensions define a state of rest, while the fourth expanding dimension defines absolute motion at c. Ergo zero rest mass implies zero rest, which implies that the photon exists entirely in the fourth dimension. Any time matter is caught in the fourth dimension, it appears as energy and moves with the veloicty c. Hence E=mc^2!

Now it is interesting that in order for an object to gain velocity, it must have energy added to it. And this adds to the object's mass, while also making it appear shorter in the three spatial dimensions (length contraction). Now that energy would exist entirely in the fourth dimension, and as the object gained more and more mass in teh fourth dimension, it would have a greater and greater probability of existing in the fourth dimension, and thus moving.

I would guess that only objects of zero rest mass can appear in the 4th dimension, as only then can all their mass be in the moving dimension. Any rest mass would imply that part of the object has a probability of being at rest in the three spatial dimensions.

Your second question is: "Secondly, the invariant planck wavelength of the radiation manifested by the expansion would seem to imply that wavelength/energy is purely *locally* determined relative to the Lorentz signature of *local* space, independant of the wavelength when emitted from a source or prior to entering a gravitational field? Doesn't this conflict with the "observed" cosmic (3D) expansion red shift & the CMB for example? This also seems to imply that a photon moving toward a centre of mass would gain energy which, correct me if I'm wrong, is not normally observed?"

The redhsift happens because as a photon moves away from a massive object, the space becomes less and less stretched, and the photon's wavelength appears longer and longer, as shown in the attached diagram; as the expansion of the fourth dimension is a constant, unaffected by gravity. The result of the constancy of dx4/dt=ic combined with the stretching of space results in time moving slower closer to massive objects, as illustrated in the figure.

And yes, when photons approach massive objects, they are blue-shifted! They gain energy!

attachments: 2_6_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf, 5_1_2_wheeler_recommendation_mcgucken_medium.jpg

Here's an interesting post of mine from an amazon thread:

Moving Dimensions Theory stipulates that there is a frame of absolute rest--the three spatial dimensions (which of course can still bend, curve, and move in the presence of mass), and a frame of absolute motion--the fourth expanding dimension.

Now MDT agrees 100% with relativity. All of relativity's mathematics (the Lorentz...

view entire post

Moving Dimensions Theory stipulates that there is a frame of absolute rest--the three spatial dimensions (which of course can still bend, curve, and move in the presence of mass), and a frame of absolute motion--the fourth expanding dimension.

Now MDT agrees 100% with relativity. All of relativity's mathematics (the Lorentz...

view entire post

Dear Dr. E,

In your attachment: :MOVING DIMENSIONS THEORY EXAMINES THE GRAVITATIONAL REDSHIFT SLOWING OF CLOCKS", you state that curved space adjacent to a massive star is stretched and "rulers closer to the star will be stretched." Maybe I'm confused or it's a semantics issue but wouldn't a ruler be relatively shortened in a gravity well near a massive object as compared to out in a void of space?

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In your attachment: :MOVING DIMENSIONS THEORY EXAMINES THE GRAVITATIONAL REDSHIFT SLOWING OF CLOCKS", you state that curved space adjacent to a massive star is stretched and "rulers closer to the star will be stretched." Maybe I'm confused or it's a semantics issue but wouldn't a ruler be relatively shortened in a gravity well near a massive object as compared to out in a void of space?

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I'm sorry, I previously added this as a reply rather than a new post:

Dear Dr. E,

In your attachment: :MOVING DIMENSIONS THEORY EXAMINES THE GRAVITATIONAL REDSHIFT SLOWING OF CLOCKS", you state that curved space adjacent to a massive star is stretched and "rulers closer to the star will be stretched." Maybe I'm confused or it's a semantics issue but wouldn't a ruler be relatively shortened in a "gravity well" near a massive object as compared to out in a void of space?

report post as inappropriate

Dear Dr. E,

In your attachment: :MOVING DIMENSIONS THEORY EXAMINES THE GRAVITATIONAL REDSHIFT SLOWING OF CLOCKS", you state that curved space adjacent to a massive star is stretched and "rulers closer to the star will be stretched." Maybe I'm confused or it's a semantics issue but wouldn't a ruler be relatively shortened in a "gravity well" near a massive object as compared to out in a void of space?

report post as inappropriate

Greetings Friends!

Would love to send you free review copies of my new books on Light Time Dimension Theory (LTD Theory):

https://www.amazon.com/gp/product/B06X93RKSY/ref=ser

ie

s_rw_dp_sw

Email me at astrophysicsmath@gmail.com and I will send you a free review copy. Thanks & best!

Dr. Elliot McGucken

Would love to do a podcast for FQXI on how...

view entire post

Would love to send you free review copies of my new books on Light Time Dimension Theory (LTD Theory):

https://www.amazon.com/gp/product/B06X93RKSY/ref=ser

ie

s_rw_dp_sw

Email me at astrophysicsmath@gmail.com and I will send you a free review copy. Thanks & best!

Dr. Elliot McGucken

Would love to do a podcast for FQXI on how...

view entire post

attachments: 5_17021835_264470727310505_6441031296795011938_n.jpg, 5_16992073_264469633977281_7860052258686985747_o.jpg

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