Search FQXi


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.

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.

Contests Home


Previous Contests

What Is “Fundamental”
October 28, 2017 to January 22, 2018
Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation
read/discusswinners

Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
Contest Partner: The Peter and Patricia Gruber Fund.
read/discusswinners

Trick or Truth: The Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
Media Partner: Scientific American

read/discusswinners

How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American
read/discusswinners

It From Bit or Bit From It
March 25 - June 28, 2013
Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American
read/discusswinners

Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
read/discusswinners

Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
read/discusswinners

What's Ultimately Possible in Physics?
May - October 2009
Contest Partners: Astrid and Bruce McWilliams
read/discusswinners

The Nature of Time
August - December 2008
read/discusswinners

Forum Home
Introduction
Terms of Use

Order posts by:
 chronological order
 most recent first

Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.

By using the FQXi Forum, you acknowledge reading and agree to abide by the Terms of Use

 RSS feed | RSS help
RECENT POSTS IN THIS TOPIC

P. wanjohi: on 1/20/09 at 15:43pm UTC, wrote Real quality arguments there! But both are correct , if you ask me: the...

Chi Ming Hung: on 12/26/08 at 11:31am UTC, wrote Oh one more thing to add... the flaws in the arguments for the Block...

Chi Ming Hung: on 12/25/08 at 5:30am UTC, wrote Oops, 1 should read: 1. E1 occurs AFTER E2 if E1 lies within the future...

Chi Ming Hung: on 12/25/08 at 5:28am UTC, wrote Just one last post for clarification and then I'm out of here. Special...

Eckard Blumschein: on 12/24/08 at 7:34am UTC, wrote Privet Doctor Petkov, When I made a comparison between Minkowski's cones...

Chi Ming Hung: on 12/23/08 at 21:03pm UTC, wrote Vesselin, It seems you didn't read carefully what I wrote. I never said I...

Vesselin Petkov: on 12/23/08 at 20:46pm UTC, wrote Chi Ming, This is my last post. I really do not understand people like you...

Chi Ming Hung: on 12/23/08 at 18:07pm UTC, wrote Vesselin, Since I regarded the flaws in your arguments as elementary,...


RECENT FORUM POSTS

ari saaput: "Pengobatan Penyakit Kencing Nanah Secara medis, Obat Kencing Nanah..." in Summer in Space

ari saaput: "Berikut Kumpulan nama obat antibiotik gonore : ciprofloksasin dapat..." in The LHC rap!

ari saaput: "Antibiotik Obat Kencing Nanah untuk penyakit gonore di apotik dengan yang..." in Is the world made of...

ari saaput: "Keluarnya cairan kuning, Obat Kencing Nanah kehijauan, putih atau bening..." in New Online Course:...

ari saaput: "Oleh karena itu, jangan lupa menerapkan gaya hidup sehat agar terhindar..." in What if string theory is...

ari saaput: "keladi-tikus keladi Tikus Rodent tuber adalah istilah ilmiah bagi keladi..." in Why This Universe?

ari saaput: "Kunyit putih memang terdiri dari 2 jenis, pertama kunyit putih gombyok atau..." in Do we really have free...

peter cameron: "screensnap of the SciMeter thread on Sabine's blog. Point is that it is..." in SciMeter: A New Way to...


RECENT ARTICLES
click titles to read articles

Usurping Quantum Theory
The search is on for a fundamental framework that allows for even stranger links between particles than quantum theory—which could lead us to a theory of everything.

Fuzzballs v Black Holes
A radical theory replaces the cosmic crunchers with fuzzy quantum spheres, potentially solving the black-hole information paradox and explaining away the Big Bang and the origin of time.

Whose Physics Is It Anyway? Q&A with Chanda Prescod-Weinstein
Why physics and astronomy communities must take diversity issues seriously in order to do good science.

Why Time Might Not Be an Illusion
Einstein’s relativity pushes physicists towards a picture of the universe as a block, in which the past, present, and future all exist on the same footing; but maybe that shift in thinking has gone too far.

The Complexity Conundrum
Resolving the black hole firewall paradox—by calculating what a real astronaut would compute at the black hole's edge.


FQXi FORUM
July 17, 2018

CATEGORY: The Nature of Time Essay Contest (2008) [back]
TOPIC: Time and Reality of Worldtubes by Vesselin Petkov [refresh]
Bookmark and Share
Login or create account to post reply or comment.

Vesselin Petkov wrote on Dec. 1, 2008 @ 10:54 GMT
Essay Abstract

In this essay, dedicated to the one hundredth anniversary of Hermann Minkowski's talk "Space and Time", I argue that physicists should face the issue of the reality of spacetime and worldtubes of physical objects for two reasons. First, this issue is not a philosophical question, as some appear to think, since the kinematical special relativistic effects would be impossible, as will be demonstrated, if the physical objects involved in these effects did not exist as four-dimensional worldtubes. Second, taking into account that worldtubes are real four-dimensional objects provides an unexpected insight into the origin of inertia, the nature of the force acting on a body supported in a gravitational field, and possibly even the nature of quantum objects.

Author Bio

Vesselin Petkov received a graduate degree in physics from Sofia University, a doctorate in philosophy from the Institute for Philosophical Research of the Bulgarian Academy of Sciences, and a doctorate in physics from Concordia University. He taught at Sofia University and is currently teaching at Concordia University. He wrote the book "Relativity and the Nature of Spacetime" (Springer 2005) and edited the books "Relativity and the Dimensionality of the World" (Springer 2007), and "Minkowski Spacetime: A Hundred Years Later" (Springer, forthcoming). He is a member of the Governing Board of the International Society for the Advanced Study of Spacetime.

Download Essay PDF File

Bookmark and Share



Gunn wrote on Dec. 2, 2008 @ 08:12 GMT
Vesselin, Privet!

I voted for you.

Gunn Quznetsov

Bookmark and Share



Cristi Stoica wrote on Dec. 15, 2008 @ 15:31 GMT
Dear Dr. Petkov,

You made an interesting analysis of the presentist view, and an eloquent explanation of the block spacetime. I liked the presentation of General Relativistic effects from the bird’s 4-dimensional view. Interesting the spacetime explanation you provide for the quantum objects. Although not presented in this essay, I also like your ideas of propulsion by manipulating the spacetime geometry.

Best wishes,

Cristi Stoica

Flowing with a Frozen River

Bookmark and Share



Peter Leifer wrote on Dec. 17, 2008 @ 08:11 GMT
Dear Dr. Petkov,

You discussion in the field of C.Rovelli touched important questions: ``What is a quantum object?" One of the attempts to find the answer you may find in my essay: ``Morphogenesis and dynamics of quantum state".

Bets regards,

Peter

Bookmark and Share



Chi Ming Hung wrote on Dec. 17, 2008 @ 23:52 GMT
Vesselin,

Continuing our discussion from the forum for Carlo Rovelli's essay...

I've read your essay. The first parts of your essay gave a pretty good summary of the instants-vs-duration, presentism-vs-eternalism and 3D-vs-4D debates among philosophers. I'm going to comment on this part first and then the rest of your essay later.

INSTANTS vs DURATION

I think the...

view entire post


Bookmark and Share



Vesselin Petkov wrote on Dec. 18, 2008 @ 17:38 GMT
Dear Gunn, Cristi, and Peter,

Thank you for your comments. I have finally managed to read your essays and will try to comment.

Chi Ming,

You raise some interesting points about "the instants-vs-duration". The same applies to space. I am naturally much more interested in the alternative Block Universe (BU) versus Evolving (or growing) Block Universe (EBU) since it the EBU that...

view entire post


Bookmark and Share



Vesselin Petkov wrote on Dec. 18, 2008 @ 18:37 GMT
Chi Ming,

I am sorry for the poor wording of "I think it is you who should correct your view"; I was in a hurry. I meant that you yourself should correct your view.

Best wishes,

Vesselin Petkov

Bookmark and Share



Chi Ming Hung wrote on Dec. 21, 2008 @ 08:11 GMT
Vesselin,

I checked the references you mentioned, but none of them refute my claim, which is that special relativity (SR) has nothing to say about whether physical objects are 3-D, 4-D, or something else (e.g. 3N-D for an N-body quantum system).

Whether it's length contraction, relativity of simultaneity or any other effects in SR, the only thing they demonstrate is Lorentz covariance, or the physicality of the Minkowski metric for space-time, which I never doubted nor disputed.

As I already argued, as long as the underlying quantum theory is Lorentz-covariant (e.g. standard quantum field theory (QFT)), the end results of the calculation for whatever phenomena will be Lorentz-covariant, and thus will satisfy all the requirements of SR.

Take the example you emphasized so much, that of the muon lifetime experiment. As is well known and well demonstrated in accelerator experiments, the behavior of the muon, including its decay and lifetime, is accurately described by standard electroweak theory. So the question is: Does the electroweak theory say anything about the muon being a 3-D object? No, not at all. The muon is described by a Dirac field with state vector at each moment in time defined in the corresponding Fock space ("moment in time" here can refer to any generic space-like hypersurfaces in space-time, per the Schwinger-Tomonaga formalism). So one can say the muon is an object in Fock space, but not 3-D or 4-D space/space-time. I believe this to be the most accurate description we have.

And I believe the same should apply to macroscopic rods and clocks, because ultimately they are nothing but correlated collection of space-time coordinates which can, at least in principle, be calculated using QFT. And since QFT is Lorentz-covariant, so should the calculated space-time coordinates of the rods and clocks be, and thus the rods and clocks should obey all of the relativistic effects of SR.

Unless you assume that SR is a more fundamental and more correct theory than QFT, I can't see how you can base your worldview on SR alone.

Bookmark and Share



Vesselin Petkov wrote on Dec. 21, 2008 @ 22:16 GMT
Chi Ming,

Please do not ignore what I asked you to answer:

See in Sec. 3 of my previous post the thought experiment version of the real experiment that confirmed length contraction. Try to explain whether the length contraction of a meter stick at rest in observer A's reference frame would be possible if the worldtube of the meter stick did not exist. More specifically, whether observer B (moving relative to A) would measure A's meter stick as a different three-dimensional meter stick whose different parts are green, red, blue, whereas A measures a red meter stick.

This single experiment is sufficient to prove that special relativity would be impossible if the the worldtube of the meters stick (in this example) were not real.

Concerning the muon experiment. Please do not ignore again the argument (it is length contraction, not time dilation!): in the muon frame the length contraction of the space distance involved in the experiment is proved experimentally - and that is possible if that distance is a 4D worldstrip. So this experiment proves the four-dimensionality of the *macroscopic* distance (you can think of a very tall post instead of space if this bothers you or raises irrelevant objections); I have repeatedly emphasized that the relativistic experiments involving *macroscopic* bodies are manifestations of the four-dimensionality of those bodies as Minkowski himself argued (you can check what he wrote in his paper although what he wrote is, of course, not an argument).

You keep ignoring this and talk about whether the muon is a 3D or 4D object. Two things. First, the question of the dimensionality of the muon arises when you consider time dilation - when you consider the muon experiment in the ground reference frame, which I did not discuss. Second, I did not discuss that since the muon is not a macroscopic particle; but I have discussed time dilation of macroscopic bodies in my book and papers (cited above) and again that effect proves that those bodies are worldtubes. You know from the last section of my essay what I think about elementary particles (like the muon).

Finally, concerning what you wrote: "Unless you assume that SR is a more fundamental and more correct theory than QFT, I can't see how you can base your worldview on SR alone."

I have already addressed this: when you calculate the length contraction of the *macroscopic* meter stick (with colors as explained above) you use *only* special relativity; it is the *only* theory that explains this experiment. No one even bothers to to think about QFT. I really do not understand why it is so difficult to understand this obvious and actual fact.

Vesselin Petkov

Bookmark and Share



Chi Ming Hung wrote on Dec. 21, 2008 @ 23:51 GMT
Vesselin,

You said "No one even bothers to think about QFT", which is perfectly OK as long as you're not talking about the basic composition of an object, but that's exactly what you're referring to when you try to say whether an object is 3D or 4D! Without referring to the basic composition of matter, which can ONLY be described by QFT, not SR alone, your question about the dimensionality of objects is simply meaningless, which is why I insisted that you need to take QFT into account when discussing the dimensionality of objects. Otherwise it's just empty theorizing with no physical content because you chose to ignore the theory which describes the basic composition of matter.

Again, I stress that SR has nothing to say about the physical dimensionality of objects because SR has nothing to say about the basic composition of objects, which belongs to the domain of QFT, not SR.

Bookmark and Share



Vesselin Petkov wrote on Dec. 22, 2008 @ 02:12 GMT
Chi Ming,

I am afraid I really do not understand - you keep refusing to answer the main question (referring to one of the arguments proving the reality of worldtubes) that I asked three times.

I prefer not to comment on this amazing statement: "Otherwise it's just empty theorizing with no physical content because you chose to ignore the theory which describes the basic composition of matter." I will leave it to the readers.

I will respond to your postings only when you clearly address the central argument of this discussion. Let me remind you that a discussion, by definition, is properly addressing arguments, not just making claims.

Vesselin Petkov

Bookmark and Share



Chi Ming Hung wrote on Dec. 23, 2008 @ 01:41 GMT
Vesselin,

I think I already answered your questions in my comments, if you care to read them more carefully. Here's a recap of my answers.

Special relativity (SR) and all of its many macroscopic manifestations (including all the examples you pointed out), are nothing but the statement that the Minkowski metric applies to the space-time events described by SR. More specifically SR...

view entire post


Bookmark and Share



Vesselin Petkov wrote on Dec. 23, 2008 @ 06:16 GMT
Chi Ming,

"I think I already answered your questions in my comments, if you care to read them more carefully."

That is not true. You have not even addressed the main argument despite that I specifically asked you three times. The posts are above and everyone can check.

Finally, at the end of your latest post you addressed it. But, unfortunately, you wrote "The elementary flaw in your argument in this case is this: You assumed that whatever the in-sync B-cameras record in a single instant of B-time, must have occurred "all at once", but this is not true. The basic lesson of SR is that we cannot talk meaningfully about two events happening "all at once" unless the space-time coordinates of the two events coincide."

I find this unfair. You have been trying to argue about relativity (taking your and my time), but you do not appear to have even a basic knowledge of it. What you wrote above demonstrates that you do not understand the very basics - relativity of simultaneity. I would suggest that you talk to a relativist. Or look carefully at the derivation of length contraction - the end points of the meter stick are measured simultaneously (at once) by each of the two observers A and B in relative motion. It was specifically emphasized in my post that the experiment with the meter stick (with lights) is an example of a measurement of length contraction (which itself is a specific manifestation of relativity of simultaneity). So, by saying there is an "elementary flaw" in that experiment you are saying there is such a flaw in length contraction and therefore in relativity of simultaneity as well.

I hope you understand that further mutually taking our time is unreasonable. However, if for some inexplicable reason you continue to claim that you see "elementary flaws", you know what you have to do - it is your obligation as scientist to expose those "elementary flaws". The experiment with lights was published in my book "Relativity and simultaneity" and a concise version in the paper "Is there an alternative to the block universe?" Complete information about the book and a link to the PDF file of the paper are available at my publications webpage.

Happy Christmas,

Vesselin Petkov

Bookmark and Share



Vesselin Petkov wrote on Dec. 23, 2008 @ 06:25 GMT
Chi Ming,

I did not write it explicitly, but I think it is clear - if you continue to see "errors" expose them by publishing a paper on that.

Vesselin Petkov

Bookmark and Share



John Merryman wrote on Dec. 23, 2008 @ 12:52 GMT
Vesselin, Chi Ming,

This discussion provides an interesting juxtaposition between Relativity and QM.

The point I make against block time/worldtubes, etc. is that the assumption time is a path along which reality travels, from past events to future ones, is an intuitive assumption which may make far more sense if we consider that only the present physically exists, this series of events actually goes the other way, from future potential to past circumstance. That measurements of space and time vary is simply evidence that information is subjective.

Time is a linear construct of a physical state that isn't necessarily linear, so it makes sense it should be measured as discrete intervals, interspersed with non-linear, probabilistic behavior, best described in scalar concepts, such as temperature.

Narrative is a useful concept for the humanities, but science needs to develop a more nuanced concept of time. Units of time go from beginning to end, as they go from being in the future to being in the past, as the process of counting them goes from one to the next.

Bookmark and Share



Chi Ming Hung wrote on Dec. 23, 2008 @ 18:07 GMT
Vesselin,

Since I regarded the flaws in your arguments as elementary, there's really no point in publishing it.

Relativity of simultaneity is a convention, and I think all relativists should know this already. Relativity of simultaneity provides a convenient way of defining what one means by "simultaneous" as measured in different reference frames, but it says nothing about whether events happen "all at once". "Simultaneous" and "all at once" here meant different things, and should not be confused. "Simultaneous" means happening at the same clock time as measured in a particular reference frame, while "all at once", means events happening/becoming together, as measured in ALL frames.

I repeat again, and this is really elementary for anybody who understands Special relativity (SR), SR says nothing about two events happen "all at once" unless the space-time coordinates of those two events coincide. Otherwise the most you can say is that one event (A) belongs to the future of the other (B) (if A is within the future light cone of B) or vice versa. If neither A nor B is in the future/past light cones of each other, we cannot say ANYTHING at all about which event happens first. One can DEFINE whether A and B are simultaneous by choosing a certain reference frame, but this is only a CONVENTION and not physical. FOR ANY SPACE-LIKE SEPARATED EVENTS A & B, SPECIAL RELATIVITY SAYS NOTHING ABOUT WHICH EVENT HAPPENS FIRST. If you dispute that, please first check any textbook in SR.

Bookmark and Share



Vesselin Petkov wrote on Dec. 23, 2008 @ 20:46 GMT
Chi Ming,

This is my last post. I really do not understand people like you who start criticizing something without trying to understand it. And even worse, without properly reading it. All your posts are an example of this including your latest post. Instead of writing really elementary explanations such as "Relativity of simultaneity is a convention" and relativistic causality, you were supposed to read that those things were addressed in my essay (p. 5):

"A similar objection against relativity of simultaneity as an argument for the four-dimensionality of the world could be the fact that in special relativity, the causal structure of space-time defines a notion of a 'light cone' of an event, but does not define a notion of simultaneity" [11]... More importantly, however, such an objection leads to the four-dimensionality of the world even faster [12], [15]"

I also invited you to look at my publications where you would have found that those issues are addressed in more detail, for example, in the papers: "Simultaneity, Conventionality and Existence" and "Conventionality of Simultaneity and Reality".

I hope you now understand why I find your posts unprofessional and unfair.

In order to try to help you at least benefit alittle from this discussion and gain some understanding let me invite you to think on the following issues:

1. Ask yourself what the physical meaning of conventionality of simultaneity is. Why does one have the freedom (for 0 < epsilon < 1) to choose which class of events to regard as simultaneous?

2. Relativity of simultaneity must be used whenever length contraction and time dilation experiments are discussed and performed. Consider any allowable convention of simultaneity and you will have again the same situation - observer A measures a red meter stick, whereas B measures green-red-blue meter stick (note that the end points of the meter stick are both outside the light cone at M of the diagram mentioned above). So try to answer to yourself the question I asked you to address several times.

Vesselin Petkov

Bookmark and Share



Chi Ming Hung wrote on Dec. 23, 2008 @ 21:03 GMT
Vesselin,

It seems you didn't read carefully what I wrote. I never said I supported the 3-D worldview, nor the 4-D one. What I suggested is that special relativity (SR) by itself is incapable of deciding this matter one way or another.

And yes I guess there's no point in further discussion here, since our main difference is that you adhere religiously to SR as the last word in determining the structure of spacetime while I do not, and it seems unlikely that either of us will change our minds.

Bookmark and Share



Eckard Blumschein wrote on Dec. 24, 2008 @ 07:34 GMT
Privet Doctor Petkov,

When I made a comparison between Minkowski's cones of past and future and the family tree of somebody which is always absolutely regular in the past but irregular and unknown in the future, I felt that Minkowski's view might be flawed.

Could there be something wrong in current theories? I was dealing with errors of my students for more than 40 years, and I am convinced having revealed serious mistakes in application of complex calculus.

I would appreciate you checking what I am claiming to have found out:

You might look into my essay 369

You will find a more general approach attached.

Who wrote an essay has three votes.

The first one who understood me was apparently Tom Ray.

See the end of his thread.

Eckard Blumschein

attachments: 7_Microsoft_Word__How_do_negative_and_imaginary.pdf, 8_Microsoft_Word__How_do_part_2.pdf

Bookmark and Share



Chi Ming Hung wrote on Dec. 25, 2008 @ 05:28 GMT
Just one last post for clarification and then I'm out of here.

Special relativity (SR) says ONLY the following in relation to the OBJECTIVE (i.e. frame-independent) order of occurrence of two non-coincident space-time events E1 and E2:

1. E1 occurs before E2 if E1 lies within the future light-cone of E2, and vice versa.

2. If E1 lies outside the light-cones of E2 (i.e. the space-time interval between E1 and E2 is space-like), the order of occurrence of E1 and E2 is INDETERMINATE, i.e. SR has nothing to say about it.

That's it, the simple facts that refute all claims that SR implies the Block Universe (BU).

SR, even just by itself, is compatible with an evolving universe as long as one doesn't confuse clock times with the order of objective becoming (a common mistake by BU proponents).

For more detailed discussion, check e.g. M. Čapek's article "Relativity and the Status of Becoming", Foundation of Physics, 5, 607 (1975):

http://www.springerlink.com/content/q742647740684223/


Bookmark and Share



Chi Ming Hung wrote on Dec. 25, 2008 @ 05:30 GMT
Oops, 1 should read:

1. E1 occurs AFTER E2 if E1 lies within the future light-cone of E2, and vice versa.

Bookmark and Share



Chi Ming Hung wrote on Dec. 26, 2008 @ 11:31 GMT
Oh one more thing to add... the flaws in the arguments for the Block Universe (BU) can be summed up this way: BU proponents substituted my statement 2 above:

(2). If E1 lies outside the light-cones of E2 (i.e. the space-time interval between E1 and E2 is space-like), the order of occurrence of E1 and E2 is INDETERMINATE, i.e. SR has nothing to say about it.

with this one:

(2BU). If E1 lies outside the light-cones of E2, then E1 EXISTS (or is REAL) with respect to E2.

but this is not what SR says at all! SR says NOTHING about the existence or reality of E1 when it's outside the light-cones of E2. Replacing the incorrect assumption (2BU) with the correct statement (2) and the BU arguments crumble...

Bookmark and Share



P. wanjohi wrote on Jan. 20, 2009 @ 15:43 GMT
Real quality arguments there! But both are correct , if you ask me: the special relativity standpoint derives from the motion of massive body as observed from certain rest frame , while the quantum mechanics describe the behaviour of such a body's constituents within space-time continuum. Dr. Petkov's innovation is the 4 dimensional worldtubes while that of Dr. Ming is the 3N- dimensionality of such worlds, both of which depart substantially from contemporary thinking.

Yet both elaborate on each other, just like general relativity describes the simultaneaous motion of all massive bodies , creating space,time and gravitation.

I find it shocking that such important ideas as those described Drs. Petkov's and Ming's could have been ignored or suppressed for so long. To what end? It is time science took its leadership role seriously

Bookmark and Share



Login or create account to post reply or comment.

Please enter your e-mail address:
Note: Joining the FQXi mailing list does not give you a login account or constitute membership in the organization.