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Age And Relativity


sigurdV

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How does measuring the age of our universe fit in the framework of relativity?

 

Isnt an exact measure equivalent to absolute time? I then expect relativity to set a limit as to how exact we can measure the age of the universe... Otherwise we could make clocks showing absolute time...Or?

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Welcome to hypography, Sigurd :) I can tell from this post and your first one on the Liar paradox that you’re a deep thinker, and look forward to interesting conversations in our forums. :thumbs_up

 

How does measuring the age of our universe fit in the framework of relativity?

 

Isnt an exact measure equivalent to absolute time? I then expect relativity to set a limit as to how exact we can measure the age of the universe... Otherwise we could make clocks showing absolute time...Or?

Measuring the age of the universe doesn’t require or create absolute time or an absolute time measuring clock, and relativity’s “no preferred frame” principle remains valid. To explain why, we need to consider carefully what we mean by “the age of our universe”, and measuring it, and what relativity’s “no preferred frame” principle really means.

 

Although the best current estimates of the age of the universe are made using the best current cosmological model (the ΛCDM concordance model), a more straightforward definition is “the age of the oldest nearby objects we can observe”. Fortunately, the physics of stars allows some them – specifically small population II ones such as HE0107-5240 – to be nearly as old as the more theoretically complicated estimated age of the entire universe.

 

Since these old stars are nearby (36,000 Ly in the case of HE0107-5240) and like nearly all nearby bodies, have small velocities relative to us, we don’t have to much consider relativistic time dilation when answering the question “If we had been around then, and started a good timer when this star first appeared in our sky, what would the timer now read?”, and by extension, “how old is the star?” and “how old is the universe?” Our answer would be “about 13,000,000,000 years”

 

In principle, though, this question, if an unusual observer, such as one zipping around our vicinity at a very high fraction of the speed of light, asked this question, relativity would have to be taken into account. For example, at 0.99 c, the answer to the question would be [imath]13,000,000,000 \cdot \sqrt{1-0.99^2} \dot= 1,800,000,000[/imath] years.

 

Answers to questions like these get even more convoluted when asked of objects very far from us, for example, when we observe a quasar or other ancient galactic object, and ask the question “how old is that body?” Because it’s far away, the image is of the body when it was very young. Taking into account distance, however, and that quasars existed only in the universe’s early history, we might consider it very old. At such great distances, such objects’ velocities relative to us, and ours relative to them, are great, so relativity should be taken into account, but as it’s almost inconceivable we and they will ever interact, we need to consider carefully the relevance of these kinds of questions and answers.

 

Explaining the real meaning of relativity’s “no preferred frame” principle is left as an exercise for the reader. ;)

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This was quoted by accident, but i dont mind reading it twice:)

 

Welcome to hypography, Sigurd :) I can tell from this post and your first one[/url] on the Liar paradox that you’re a deep thinker, and look forward to interesting conversations in our forums. :thumbs_up

 

 

Measuring the age of the universe doesn’t require or create absolute time or an absolute time measuring clock, and relativity’s “no preferred frame” principle remains valid. To explain why, we need to consider carefully what we mean by “the age of our universe”, and measuring it, and what relativity’s “no preferred frame” principle really means.

 

Although the best current estimates of the age of the universe are made using the best current cosmological model (the ΛCDM concordance model), a more straightforward definition is “the age of the oldest nearby objects we can observe”. Fortunately, the physics of stars allows some them – specifically small population II ones such as HE0107-5240 – to be nearly as old as the more theoretically complicated estimated age of the entire universe.

 

Since these old stars are nearby (36,000 Ly in the case of HE0107-5240) and like nearly all nearby bodies, have small velocities relative to us, we don’t have to much consider relativistic time dilation when answering the question “If we had been around then, and started a good timer when this star first appeared in our sky, what would the timer now read?”, and by extension, “how old is the star?” and “how old is the universe?” Our answer would be “about 13,000,000,000 years”

 

In principle, though, this question, if an unusual observer, such as one zipping around our vicinity at a very high fraction of the speed of light, asked this question, relativity would have to be taken into account. For example, at 0.99 c, the answer to the question would be [imath]13,000,000,000 \cdot \sqrt{1-0.99^2} \dot= 1,800,000,000[/imath] years.

 

Answers to questions like these get even more convoluted when asked of objects very far from us, for example, when we observe a quasar or other ancient galactic object, and ask the question “how old is that body?” Because it’s far away, the image is of the body when it was very young. Taking into account distance, however, and that quasars existed only in the universe’s early history, we might consider it very old. At such great distances, such objects’ velocities relative to us, and ours relative to them, are great, so relativity should be taken into account, but as it’s almost inconceivable we and they will ever interact, we need to consider carefully the relevance of these kinds of questions and answers.

 

Explaining the real meaning of relativity’s “no preferred frame” principle is left as an exercise for the reader. ;)

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Thank you for a kind and very constructive answer! I shall now proceed to consult a study on relativity. The moment i get stuck I will not hesitate to ask, after all... those things contain Mathematical Formulas!

 

Meanwhile there is something i would like to ask you before climbing "Mount Einstein":

Is there (in physics and/or mathematics) a precise definition of "Frame" or is it an intuitive concept?

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Thank you for a kind and very constructive answer! I shall now proceed to consult a study on relativity. The moment i get stuck I will not hesitate to ask, after all... those things contain Mathematical Formulas!

Congratulations, and good luck! Relativity is, I think, one of the most scientific theories and general concepts there is, and a sound understanding of it essential for any thoughtful person of our times.

 

Meanwhile there is something i would like to ask you before climbing "Mount Einstein":

Is there (in physics and/or mathematics) a precise definition of "Frame" or is it an intuitive concept?

A discussion of this question is well underway at A Theory Of Frames?.

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Readers perhaps should not need to jump between topics, so here also is found my reaction while reading a thought experiment supposed to show that instanteous signals,were they to exist, in certain circumstances could signal back in time:

 

The space traveling twins Max and Maxine are receeding from one another at 90 percent of light speed, and are presently 1.1 light-years apart. Max in the year 1990 sees, because of the sync shift, that Maxines calenders say 1988 Two full light years behind his own way of telling time. If he sends an instantious signal it always stays in 1990 in his frame but it arrives at Maxine's frame in 1988. Because of the same sync shift effect,Maxine, as she recieves Max's signal in the year 1988, sees that Max's calendars say 1986: from Maxine's point of view, it is Max who is two years behind.If Maxine now returns Max's signal instantaneously, the signal will arrive back ay Max's ship in 1986.Using Maxine as a relay Max is able to signal 4 years back into his own past!

 

It will take some effort convincing me that an instantious signal sent in a frame 1990 can hit another frame in 1988! Such a signal is not "instantaneous", it is travelling backwards in time!

 

Surely a signal is instantaneous if, and only if, the age of the universe, in the event it is sent from and in the event it is recieved in, is the same... Then we speak of the events, in a natural way, as being simultaneous.

 

I believe Scientists try to construct precise definitions using only so defined terms. The following is then perhaps not the last word of Relativity concerning "Simultaneous":

 

Two events occurring at points p and q of an inertial frame F are simultaneous if and only if light emitted at the two events arrives simultaneously at the midpoint of the segment pq in F.

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The Theory of Relativity Stands (and falls) on two legs:

 

1. The speed of light in vacuo is propagated rectilinearly with the same constant velocity c (approximately 300000 km/sec) at all times,in all directions, and in all inertial frames.

 

2. An inertial frame f1 in uniform translatory motion relative to an inertial frame f2 cannot be distinguished from f2 by any physical experiment whatever. (The no preferred frame principle)

 

The reader protesting that it cant be all, since books on Relativity are thick and tightly packed with strange objects like matrices and tensors, can rest assured that above is what IS the Theory of Relativity! The rest is definitions, consequences, assumptions and explanations.

 

Is it now not obvious why Relativity is a Theory of Frames?

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The Theory of Relativity Stands (and falls) on two legs:

 

1. The speed of light in vacuo is propagated rectilinearly with the same constant velocity c (approximately 300000 km/sec) at all times,in all directions, and in all inertial frames.

 

2. An inertial frame f1 in uniform translatory motion relative to an inertial frame f2 cannot be distinguished from f2 by any physical experiment whatever. (The no preferred frame principle)

Correct! :thumbs_up ... with one important clarification. These two postulates, known traditionally as the principle or relativity and the principle of invariant light speed, together are the only postulates needed to formulate special relativity.

 

SR provides a complete description of the motion of bodies unaffected by gravity. It’s wise to begin studying relativity with SR, as the mechanics of a system without gravity are much simpler than of one with it – all full of nice, straight lines, rather than the real universes complicated curves.

 

The full theory of relativity includes general relativity. It adds a 3rd postulate, traditionally known as the equivalence principle:

 

3. There is no way for an observer to distinguish locally between gravity and acceleration.

GR expands SR’s description of the motion of bodies to include the effects of gravity. Using GR – actually performing calculations to predict and explain the motion of bodies – is much more complicated than using SR.

 

(sources: the wikipedia article Special relativity and the University of Oregon webpage Relativity

 

The reader protesting that it cant be all, since books on Relativity are thick and tightly packed with strange objects like matrices and tensors, can rest assured that above is what IS the Theory of Relativity! The rest is definitions, consequences, assumptions and explanations.

You’ll hear no such protest from me, or, I think, from anyone with a modicum of academic of self-acquired education in modern physics. The “strange objects” you describe might, I think, be better described as “unfamiliar objects”. Once they become familiar, their description usually changes to “useful tools”. :)

 

The essence of relativity, however, is simply the 2 (if you don’t need to consider gravity) or 3 (if you do) postulates we’ve listed above. It’s intensely simple and intuitive. The consequences of these postulates are not simple or (at least at first brush) intuitive.

 

Is it now not obvious why Relativity is a Theory of Frames?

If you find this a useful metaphor for studying relativity, I recommend you keep and enlarge it. I don’t find it especially illuminating, but that’s the nature of metaphor: different people find different metaphors for the same objective phenomena more or less useful.

 

Readers perhaps should not need to jump between topics, so here also is found my reaction while reading a thought experiment supposed to show that instanteous signals,were they to exist, in certain circumstances could signal back in time:

 

The space traveling twins Max and Maxine are receeding from one another at 90 percent of light speed ...

I recommend keeping away from this subject – potentially causality violating signaling into the past – until your practical grasp of the mechanics of SR feels solid. When your grasp is at that level, you should be able to use SR to answer common textbook questions quickly, easily, and intuitively. Here are a few such questions:

 

  • Alice and Bob are together with zero relative velocity at time t=0 according to both their clocks. Alice suddenly accelerates to a speed of 0.9 c as measured by Bob, travels for 1 hour according to her clock, then suddenly changes velocity to 0.9 c in the opposite direction, returns to Bob’s location, and suddenly changes velocity to zero. Bob and Carol compare their clocks. What do they read?
     
  • Alice, Bob and Carol are together with zero relative velocity at time t=0 according to their clocks. Alice suddenly accelerates to a speed of 0.9 c as measured by Carol, travels for 1 hour according to her clock, then suddenly changes velocity to zero. At 1 hour according to his clock, Bob suddenly accelerates to a speed of 0.9 c in the same direction Alice did,travels for 1 hour according to his clock, then suddenly changes velocity to zero. Bob and Carol (who are now together with zero relative velocity) compare their clocks. What do they read?
     
    At 2 hours according to her clock, Carol sends a radio message to Bob and Alice. When they receive it, what do their clocks read?

That said, to the best of my knowledge, 2 non-accelerating bodies can’t signal into their pasts using faster than light (including infinitely fast, instant signals) in the way you describe. A very well explanation of how this can be done with 4 bodies can be read at Sharp Blue: Relativity, FTL and causality – but again, I caution you not to spend too much time at this unless you’re comfort level with introductory-level SR use is high.

 

:QuestionM You mention that you read the “Max and Maxine” though experiment you shared. Can you post a link to where you read it?

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Hi Craig:)

Modern man assumes everythings on the net...sorry, see the book:Faster than light by Nick Herbert,Ph.D.

 

Thanks for the four bodies tip! It will be a pleasure to check, i dont expect to find the error in the calculations since mathematicians are quick to point them out, it will probably be in some hidden assumtion.

 

Why I expect an error is made?

 

Well, since by definition (Instant signals neither reaches future nor the past) instant signals dont travel to the past, the only way to find them there is using inconsistent theory!

 

I think frames are useful but relativity is about a restricted subclass only of interest to physics, perhaps excepting frames of ordinary experience and the universal frame if they are to be found in there. Concepts like "Frame", "context" and "concept" belong,alas, to the now extinct science of Semantics.

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Well, since by definition (Instant signals neither reaches future nor the past) instant signals dont travel to the past, the only way to find them there is using inconsistent theory!

On the contrary, instant signals must arrive before they were sent (from the receiver's perspective). That you assume instantaneous communication is possible is the inconsistency, as illustrated in CraigD's link to Sharp Blue.... Your proposition violates causality, though it isn't readily obvious.

 

Classical mechanics assumes time (and therefore simultaneity) to be invariant. If this were true, then the speed of light would vary depending on the inertial frame of the observer. Special Relativity is a consequence of the fact that the speed of light is invariant, no matter the observer's velocity (frame). This fact is so well tested that anything arguing differently can almost immediately be thrown out as woo. The consequences of this become more apparent when you look at Lorentz transformations. Here is a short youtube video that should make the difference between a Galilean transformation and a Lorentz transformation clearer.

 

 

Given these transformations, it should be clear that "frame" is roughly equivalent to "perspective". The driver of a passing car hears a different sound when he honks his horn than a person on the side of the road because the two are in different frames. Though sound travels much slower than light, the speed is closer to our everyday experience, so sometimes it may be useful to substitute sound for light when you are visualizing a problem that involves changing perspectives, or frames of reference.

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Well, since by definition (Instant signals neither reaches future nor the past) instant signals dont travel to the past, the only way to find them there is using inconsistent theory!

Even assuming that an instant of faster-than-light signal is physically possible, your “definition” disagrees with the theory of special relativity. Taken intuitively, disregarding what’s been known for about 140 years, it makes sense, but such intuitive knowledge isn’t scientific.

 

Special relativity not only predicts that clocks tell different time depending on their relative velocity, it predicts that events that appear simultaneous to one observer do not appear simultaneous to another. The simplest illustration I know of this is the “ladder paradox” thought experiment. this wikipedia article has as nice a presentation of it as I’ve seen.

 

These predictions are intensely counter-intuitive, but the purpose of “paradoxical” though experiments like the above are not to convince students to reject special relativity, but to understand that our intuition, acquired unconsciously through experiencing everyday events, which involve relative speeds that are very small fractions of the speed of light, is not a reliable for physics involving relative speeds that are appreciable fractions of the speed of light.

 

Again, I strongly recommend acquiring an introductory knowledge of Special Relativity before considering complicated implications such as causality violating signaling into the past via faster than light signal carriers. You wouldn’t try to climb Mt Everest before learning basic mountain climbing techniques, so shouldn’t approach complicated modern physics without learning their basics. You’ll know you know the basics by being able to answer questions like those in my previous post.

 

(italics mine)

I think frames are useful but relativity is about a restricted subclass only of interest to physics, perhaps excepting frames of ordinary experience and the universal frame if they are to be found in there.

The essence – the first postulate – of special relativity is that there is no such thing as “the universal frame”. Physicists aren’t at all interested in it, because they almost universally understand it doesn’t exist.

 

Search science literature, Sigurd. I believe you’ll discover that this concept was practically entirely discredited about 100 years ago. The clearest explanation of why, I think, can be found by thoroughly understanding “the most famous/important failed experiment ever”, 1887’s Michelson–Morley experiment, which sought, and dramatically failed, to detect “the luminous ether”, which I believe refers to the same hypothetical entity that you mean by “the universal frame”.

 

Concepts like "Frame", "context" and "concept" belong,alas, to the now extinct science of Semantics.

If the concept of “frame”, “context”, and “concept”, seem un-useful to you, simply don’t use them. They aren’t necessary for the exercise of calculating results using the mechanics of special relativity. If you complete such exercises, acquiring about the level of working knowledge a college freshman or sophomore, or an advanced class-taking high school or earlier student would in the course of an "introduction to modern physics" class, I believe you’d find these concepts useful, but if you chose to never think of them, you’d still be able to perform the relativistic calculations.

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Hi!

First: I dont deny the existence of relativistic effects, its too bad that im not able myself to calculate them (yet), but I can understand arguments and definitions: I find it hard to believe that there is in Special Relativity no better definition of simultanity than the following circular one?

 

"Two events occurring at points p and q of an inertial frame F are simultaneous if and only if light emitted at the two events arrives simultaneously at the midpoint of the segment pq in F."

 

Second: Explanations of Relativity sometimes makes too far reaching claims in defending it:

 

"The essence – the first postulate – of special relativity is that there is no such thing as “the universal frame”. Physicists aren’t at all interested in it, because they almost universally understand it doesn’t exist."

 

So there IS no Multiverse? It is now proven to be a non possible non Einsteinian frame for our universe? This is News! Give me a link please! (But I admit i did not express myself clearly there, making no distinctions between Relativity,Observators and Cosmology.)

 

Third: Unless Relativity denies the existence of the present, the past and the future of an event, definitions using the concepts should be permitted in discussions!

 

(In discussions like this one it is sometimes forgotten that Relativity is not a theory about everything: There is,for example, Quantum Theory which sounds even stranger to the uninitiated than Relativity...)

 

Whether "my" definition of "instant" signal clashes with the Relativistic Definition or not, I cannot tell since I have not seen one yet. Perhaps there is none?

 

Looking at the Max/Maxine Thought experiment where Max seeing Maxine in her past sends an "instant" signal to that past "forgetting" that he should wait until Maxines "present" comes into his wiew before he can see the signal arriving to Maxine, makes me wonder:

 

If one instantly takes away our sun, dont we have to wait a little to see the result?

 

Or does "Instantly" MEAN "At the time in the past when the result of the act would be visible right now"?

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I find it hard to believe that there is in Special Relativity no better definition of simultanity than the following circular one?

 

"Two events occurring at points p and q of an inertial frame F are simultaneous if and only if light emitted at the two events arrives simultaneously at the midpoint of the segment pq in F."

 

You find it hard to believe because you are still stuck in the classical mindset with absolute time and universal simultaneity. The definition is not circular, it just means observers at differing velocities will have a different perspective of what events occur simultaneously.

 

Second: Explanations of Relativity sometimes makes too far reaching claims in defending it:

 

"The essence – the first postulate – of special relativity is that there is no such thing as “the universal frame”. Physicists aren’t at all interested in it, because they almost universally understand it doesn’t exist."

 

So there IS no Multiverse? It is now proven to be a non possible non Einsteinian frame for our universe? This is News! Give me a link please! (But I admit i did not express myself clearly there, making no distinctions between Relativity,Observators and Cosmology.)

Frankly, I do not understand how you made the logical connection that the absence of a universal frame disproves the multiverse hypothesis. If you were to explain how you came to this conclusion, it might shed light on where you are going wrong conceptually.

 

Third: Unless Relativity denies the existence of the present, the past and the future of an event, definitions using the concepts should be permitted in discussions!

No one is claiming otherwise. I'm at a loss. Invariant speed of light makes absolute time, absolute distance, and universal simultaneity incorrect, but in no way throws out the concepts of past, present, or future.

 

Whether "my" definition of "instant" signal clashes with the Relativistic Definition or not, I cannot tell since I have not seen one yet. Perhaps there is none?

If there was an instant signal, it would contradict causality. Maxine would receive the signal before Max sent it. Do you have a link to this thought experiment, or is it from a book?

 

It appears to me that you are still hung up on simultaneity. If that's the case, I recommend reviewing the links in this thread. I don't want to add too many more and bog you down until I have a clearer picture of what you don't understand.

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Actually it is a lot of things at once...but dont worry i will read and think about it all!

I appreciate being busy. SO! The definition really is the definition used in relativity and it is not circular?

The word to be explained is "simultaneous" and it occurs on the left side of an implication "if and only if" right? So what is "simultaneously doing there on the right side of same implication?

Uh..yes i guess im hang up on simoultaneity, if I dont understand I dont forget and go on assuming I understand (I hope) I think I understand what simoultaneity means as I tried to show with my example about instant destruction of our sun...I notice it is as yet not noticed and commented:)

 

The Max/maxine experiment is from the book "Faster Than Light" by Nick Herbert Ph,D.

 

I triplechecked before I put it in here...it IS an honest citation! (I checked again, and Ill check the experiment CraigD mentioned later, but first id like to be convinced Relativity is not killing a charichature of simultainety.It should not matter to it whether observators disagree on it, all that shows us is they cant measure it properly!)

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Well, it's your wording. If you don't like it, try "Two events occurring at points p and q of an inertial frame F are simultaneous if and only if light emitted at the two events arrives at the same time at the midpoint of the segment pq in F."

 

The point is that what is simultaneous in frame F (F's perspective) is not simultaneous in different frames. Again, this is a direct consequence of the invariant speed of light, as demonstrated in the youtube clip I posted above.

 

EDIT: I am a visual learner. In case you are as well, I think this youtube clip may do a better job than the one I linked to previously in showing how time, distance, and simultaneity are frame dependent.

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Uh..yes i guess im hang up on simoultaneity, if I dont understand I dont forget and go on assuming I understand (I hope) I think I understand what simoultaneity means as I tried to show with my example about instant destruction of our sun...I notice it is as yet not noticed and commented:)

 

I apologize, somehow I missed this last night. If the sun were to instantly disappear, in Newtonian mechanics (universal time), everything orbiting the sun would immediately fly off at a tangent. However, in relativity, it would take eight minutes for the "signal" of the absence of the sun to reach the Earth, and then we would fly off into space. Notice, if Newtonian mechanics were correct, causality would be violated, as the Earth would fly off eight minutes before receiving the last light from the sun.

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First: I dont deny the existence of relativistic effects, its too bad that im not able myself to calculate them (yet), but I can understand arguments and definitions

Best wishes regarding your physics education, Sigurd! :thumbs_up Hopefully we hypographers can help it along.

 

I believe you’ll encounter some epistemological revelations along the way, for the most part not overtly stated in physics texts, and only difficultly stated in philosophies. Key among these is the dramatic difference in lexicon cardinalities of the mathematical language of physics and the natural language used to explain it non-mathematically. Though a precise count is difficult and controversial to arrive at, physics has on the order of 10 to 100 “lexemes”, depending on whether your formalism is classical (including special and general relativity) or quantum physical. Natural language has on the order of 1000 times as many. Attempting to match natural language definition to physics can thus be problematical. In the course of acquiring a mathematical “vocabulary”, many students practically abandon the attempt, other than when needed to explain physics to people lacking the requisite math vocabulary.

 

I find it hard to believe that there is in Special Relativity no better definition of simultanity than the following circular one?

 

"Two events occurring at points p and q of an inertial frame F are simultaneous if and only if light emitted at the two events arrives simultaneously at the midpoint of the segment pq in F."

This definition is only circular, I think, when expressed in a natural language manner like this, and parsed very a-contextually. The sentence does reduce to a circular “<noun> are simultaneous if and only if <verb> simultaneously”, but this analysis fails to appreciate the key distinction between the physical referents of the two occurrences of the “simultaneous” lexeme: the first refers to events that a separated by a large distance, the second to events separated by a small distance, important distinctions in the mechanics of special relativity.

 

This failure also, I think, underlies your intuitive rejection of the relativity of simultaneity, Sigurd, because that intuition is informed by experience with the application of the “simultaneous” lexeme only to events separated by small distance and time-measured with low precision.

 

I’m saying essentially the same thing JM did, in a couple of sentences, here:

You find it hard to believe because you are still stuck in the classical mindset with absolute time and universal simultaneity. The definition is not circular, it just means observers at differing velocities will have a different perspective of what events occur simultaneously.

 

The Max/maxine experiment is from the book "Faster Than Light" by Nick Herbert Ph,D.

You’ve renewed my interested (an launched me on a search for books by and about them old and new) in Nick Herbert, Fred Wolf, Jack Sarfatti, and their whole 1970s Lawrence Berkley “Fundimental Fysics Group” crew. I was sketchily aware of these and similar folk, from reading The Dancing Wu Li Masters, and from pretty much being an undergrad version of them, ca. 1980. My own faith in what I think is best termed “quantum mysticism” waned to nothingness in the mid 1990s, due in most part to my following of literature of quantum computers, which lead me to unexpected contradictions of quantum mysticisms key tenets – but I digress badly from the topic at hand: special relativity, which is a classical, not a quantum mechanical theory (though it’s rigorously applied to and not in principle contradicted by quantum mechanics) – and digress again into the subject of the relationship of relativity and quantum mechanics! ;)

 

So back to relativity...

 

… but first id like to be convinced Relativity is not killing a charichature of simultainety.It should not matter to it whether observators disagree on it, all that shows us is they cant measure it properly!)

I expect you’ll be, with enough study, convinced.

 

Special relativity doesn’t “kill” the concept of simultaneity, or show that we can’t measure it properly. Rather, it provides simple mathematical tools and guiding insight in their use to allow us to precisely resolve the paradoxes that arise from the intuitively assumed absolute simultaneity of the older, Galilean/Newtonian relativistic physics. It shows that simultaneity does depend on the relative velocity of the observer measuring it, while allowing us to calculate what order of events any given observer would measure. When relativity states “there are no privileged/universal inertial frames”, it refers to this “equality among inertial frames”. Because we can precisely describe the measurement of phenomena for any inertial frame, there’s no reason to prefer any one over any other, freeing us to write physics in whatever frame is most convenient for the work at hand.

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