Fundamental Valid Frame of Rest

[Wes Tausend]

...

Three scientists are familiar with Special Relativity and it's rules.

The three scientists decide to conduct a Special Relativity experiment. The plan is for two of them to get into two separate rocket ships and pass one another nearly head-on overhead while the third scientist observes from a base upon earth.

They decide to first pass one another, each traveling at exactly 1/2 the speed of light, as measured by the observer on the ground. Later, during debriefing, they discuss each personal frame of reference. Because they believe in the tenets of SR, each believes that he or she can regard their own frame of reference as being at rest, while at the same time acknowledging so to can the other two make a similar claim.

No one has exceeded the speed of light relative to another. Even though the two rocket pilots seem to approach and pass one another exactly at the speed of light, all frames of reference are still valid, even if they must be considered separately, are they not?

Thanks,
Wes
...

 

[Fredrik]

The title of this thread is misleading, since your thought experiment doesn't have anything to do with a fundamental rest frame.

My only objection to what you said after the title is to the phrase "pass one another exactly at the speed of light". The third observer would describe the distance between the rockets at shrinking at a rate of exactly c. But each of the two rocket pilots will describe the other one as approaching with speed (in units such that c=1)
$$\frac{\frac 1 2+\frac 1 2}{1+\frac 1 2\cdot\frac 1 2}=\frac{1}{1+\frac 1 4}=\frac 4 5.$$
In other words, 80% of the speed of light.

If the two rockets speed up further, then the "closing speed" (i.e. the rate at which the distance between the rockets is shrinking) in the third observer's rest frame, will be greater than c. But the speed that each pilot assigns to the other rocket is always less than c.

 

[Nugatory]

...
No one has exceeded the speed of light relative to another. Even though the two rocket pilots seem to approach and pass one another exactly at the speed of light, all frames of reference are still valid, even if they must be considered separately, are they not?

They are all equally valid, but I'm not sure what you mean by "must be considered separately".

Because of the way that relativisitic velocity addition works, each rocket pilot, considering himself to be at rest, sees the ground observer approaching at .5c and the other rocket approaching at .8c

They will all agree that any light signal, no matter which observer emits it and which observer receives it, has covered the distance between the point of emission and point of reception at speed c.

 

[jtbell]

Even though the two rocket pilots seem to approach and pass one another exactly at the speed of light

The two rocket pilots do not "see" each other traveling at that speed. Look up "relativistic velocity addition:"

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html

The second box on that page (Relativistic Relative Velocity) is exactly your situation.

From the point of view of the observer on the earth, the distance between the two ships does change at a rate equal to c. However, this is not the velocity of either ship in any inertial reference frame, but merely the difference between two velocities. We sometimes call this a "closing velocity" or "separation velocity". Its magnitude can be as large as 2c.

[added: wow, three virtually simultaneous responses!]

 

[Meir Achuz]

"Even though the two rocket pilots seem to approach and pass one another exactly at the speed of light"
NO.
Relative velocity in Special Relativity (The similarity of the two words is not accidental.) is the speed of one object as measured in the rest system of the other.

 

[Wes Tausend]

...

Fredrik,
I'm sorry I used the term, "Fundamental", if it has some other specific meaning. Maybe I should have labeled the post Fundamentals: Valid Frame of Rest. I still have a troubling question in mind, on assigning rest that is very fundamental (I think). I agree the two pilots can only approach at 80% C as relative to one another, by the rules.

Nugatory,
What I mean by, "must be considered separately", is that each can calculate his velocity , or speed, separately relative to the others. To conveniently describe his personal conclusion of relative interactions with the other two while traveling, I think he "must" regard his own position as rest. Perhaps I could have said "may" instead of "must". I agree that all will regard the speed of C the same between any two points of "emission" and "reception" (or source vs destination).

jtbell,
I agree the two rocket pilots do not "see" each other approaching while traveling at that speed. I'm not sure, but I think they might see each other receding after they have passed. Thanks for the link; it is exactly my situation above, somewhat validating my first question. Yes, they could agree during debriefing that they could approach at nearly 2c, each limited by the maximum speed any rocket may obtain and this particular earthly observer, I believe.
======================================================================

The following is a very difficult question to ask.

I'm kind of worried how this additional query will be received and I've tried to choose my words carefully. I'm kind of way out of the box here, and I apologise if I've gone too far. Observing the two aforementioned "lightspeed" rockets, and discussing their rest relationships is similar to my next observation and question, but not quite the same.

My next "frame of rest" question is extraordinarily fundamental and is this. Can I assign a pinpoint source of light as a frame of rest while some matter moves away from it at speed C? I know it is a very unusual perspective. I guess it would be like Einstein riding a light beam and considering himself at rest. Can light itself be a valid frame of rest? Is Relativity itself relative? I know that sounds dumb to ask, but I've mulled it over for years and never resolved it.

I confess that I imagine the above, and the unusual perspective seems to make my visual understanding of Special and General Relativity quite a bit easier. In the end, it seems I can picture it better which I try to explain below. But I am not sure it is a valid perspective. I tried to reason it out myself, but I probably missed something(s). I don't have a formal advanced education, but the geometry of spatial dimension comes fairly easy to me.

My unusual perspective is to imagine shining a flashlight at a wall as a thought experiment. We always consider that the flashlight is the source of light and perhaps the wall it's destination. But a peculiar property of light is that it takes no time at all from source to destination. It seems arbitrary to me to always assign light an "absolute direction" since it exists at source and destination at exactly the same time. So which is which, or does it even matter?

Other than the convenience of choosing an arbitrary frame, how do I know what "true" motion I am observing when I observe the flashlight and the wall? Perhaps the wall is moving at a tremendous speed away from the flashlight, or perhaps the other way around. If I were to measure and remeasure this, and each time I find that the speed is the same, I might conclude either; that either the wall, or light, moves at a constant speed (C) relative to the other. Summarily, I may be able to pick either as a valid frame of rest according to my own convenience. This may not seem initially useful, but I hope it is logical for now.

I think my "visual advantage" in looking at the "wall situation" in this "backwards" Special Relativity way is that Michelson and Morley finally seem to find their sought after Absolute Rest. Absolute Rest becomes light which may be now assigned zero speed (rest) throughout the "alternately perceived" universe.

Unfortunately matter and space would then become a non-ending explosion, at velocity C, of vacuum and atoms. It is not unlike imagining the Big Bang, but more like a "constant little bang" that never quits. As an example, the less restful, but "solid" atom dimensions in my computer as I type this, would fall somewhere between the extreme relative motions of a Super Nova and Black Hole, and not quite as still as I normally prefer when I consider myself to be at rest. On the other hand, it is easy to imagine that humans, and their extraordinarily sparse atomic nature, would be incredibly lucky to be exactly at rest, even dimension-wise, so that makes it less alarming as a blatant untruth. Logically, we may be both as per SR. I think.

Since nothing can move faster than C, any added motion of high speed matter (the still wall, or a moving rocket) must be assigned a deceleraton in order to approach (return?) towards the zero speed of light. At the "zero" speed of light, at least the forward dimension of matter must cease (collapse entirely). In other words, in this "backwards" perspective, nothing can move slower than light, which is zero and a very palatable speed barrier to visualise. There is no sense in mentioning all points now, but other things in General Relativity become easier for me to visualise also.

As long as everything does, and can, remain "perfectly backwards", I unable to see where any rules of Special Relativity are broken. As an example, one may write E=M(-C²), and it is mathematically identical to E=MC². Either directional perspective of light seems logically just another valid, but reversable part of Einstein's same relativity theories. I think. I hope.

I apologise for this long post. I hope this isn't too overwhelming to envision or think about answering. It took me quite a while to become accustomed which is understandable, I'm sure.

So can I legitimately do this if it sometimes helps me visualize some parts of Special and General Relativity better, or do I mislead myself by breaking some immutable physics rule(s)?

Thanks,
Wes
...

 

[DrGreg]

We have an FAQ on that: Rest frame of a photon

 

[Nugatory]

.I'm not sure, but I think they might see each other receding after they have passed.

Yes, at the same .8c that they were approaching before they passed. This is exactly the same situation as me standing by the road while you drive by at the more mundane speed of 100 km/h; you appear far in teh distance moving towards me at 100 km/hr, you get closer, you pass me, you recede into the distance at 100 km/hr.

My next "frame of rest" question is extraordinarily fundamental and is this. Can I assign a pinpoint source of light as a frame of rest while some matter moves away from it at speed C? I know it is a very unusual perspective. I guess it would be like Einstein riding a light beam and considering himself at rest. Can light itself be a valid frame of rest?

DrGreg has already pointed you at the FAQ on this topic. The only thing I can add is that one of the postulates of SR is that light travels at the speed of light in all inertial frames; therefore in SR there are no frames in which light is at rest.

People sometimes fool themselves by trying to set $v$ equal to $c$ in the length contraction and time dilation formulas just to see what would happen, and then they come up with conclusions such as your "a peculiar property of light is that it takes no time at all from source to destination". The problem is that the derivation of the formulas depends on there not being any frame in which the speed of light is not $c$, so setting $v=c$ invalidates the results.

But a peculiar property of light is that it takes no time at all from source to destination.

Not so... For any observer, anywhere, the time it takes for light to get from source to destination is the distance between the source and destination, divided by the speed of light.

 

[Wes Tausend]

We have an FAQ on that: Rest frame of a photon

DrGreg,

Sorry for the delay in answering and thank you for the succinct "Rest frame of a photon" link.

It has taken me a while to reply because I'm grappling with two difficult problems here. One is what I hope to be, a visual aid to understanding the Relativities, and the other, far more difficult, is how may I properly word a permissible condensed version of my question(s) here on this forum. Physicforums is almost a lone oasis of openly available skill and knowledge on the subject. If not here, I fear I may not get another chance to inquire of this in a professional setting.

It may be unfortunately apparent that despite your linked "rest of a photon" post, light at rest does make sense to me in a controverted way. I'm just not sure I can present it within the confines of SR, but let me try just once more and then I will give up. I apologise for the length of the post.

Although light does not stand still as we measure it, it does serve as our supreme alternate anchor to rest, which is very similar, and that is why C worked so well for Einstein in the absence of Absolute Rest. To me, light is the best rendition of Absolute Rest that we can have. But then everything else must be somehow moving at C.

Because the following two are most often considered different theories, I am loathe to do it here, but I can make an analogy with heliocentricity vs geocentricity. If we are allowed to apply Mach's Principle, I regard that either may be considered valid for purposes of a thought experiment. Unfortunately, comparison of separate theories as the same incident may put me further outside Relativity, not healthy on this forum.

To make an analogy with heliocentricity vs geocentricity, heliocentricity is difficult to visualize from an earthbound "rest" position. But if an observer places him or herself outside the solar system... if it is/was permissible for a rogue observer to leave "home"... it is easy to visualize. In the pre-helio days it was difficult to describe that Earth rotated in what might be considered a negative direction to the sun (or positive in the solar system, take your pick) and common internal observation just seemed to reveal that the sun did all the moving. By placing oneself uncommonly far from home, outside the solar system, one may assume to be an outside observer "at rest" with the sun, the very same sun that all other internal observers are so sure is moving.

If we didn't understand how the solar system works today and a forum member came on here today to explain it, he might inadvertently be told that "it doesn't make sense" and all this talk of a "rested sun" is rubbish. Such a member might be thrown off the forum, which is of course, my biggest fear right now. I am not absolutely sure the analogy is proper and within the bounds of SR, but it might be since all mirror images are so very much similar. And that is the crux of my dilemma regarding inclusion of my "backwards" visual aid in SR.

First, in my imaginary thought experiment, I regard light normally at C, but equally valid to -C (negative 299792458 m/s) in internal, everyday, "Michelson and Morley", at-home, observing experience. That is what I somewhat insanely questioned earlier of which is moving, the wall, or the light beam. Perhaps the true direction of a trail of light is backwards until proven otherwise. And finally, the interpretation probably doesn't matter, as the two directions of this constant seem to be interchangable anyway. E=MC² is simply equal to E=M(-C²).

But, getting back, independently observing the same event from outside the universe, I might regard the light beam at zero speed as the same incident is viewed by an independent outside observer, if "being outside the universe" makes any sense, or is even permissible within Relativity. It certainly seemed permissible within the laws of classic physics and the solar system.

In the inside "home" view, the quantity of C as measured has not changed, only the quality (supposed arbitrary relative direction). From the outside of the universe, far from "home", I imagine an independent supposed observation rest position with that of light also at rest. I imagine only the independent "outside" observer sees light stand still as the matter always continues to explode (including scientific rulers) at rate C in it's fury of scattering momentum. I hope this confusing relationship has become more clear in view of the preceeding solar system analogy.

Second, concerning the direct of light, I note that in the second postulate, Einstein refers to an "...as measured... definite velocity c..." and also "OR: The speed of light...". I take it his intent with the first term, "velocity", is to assume absolute direction, and in the second sentence, alternately require no defined absolute direction in his mention of the similar term, "speed". I'm not quite sure if that makes any difference between C and -C, since one (velocity) connotes direction and the other (speed) does not. Obviously I would have preferred Einstein used the term "speed" exclusively... but he didn't. I'm looking for some way to at least demonstrate that the rippling trail of light may go either way, hopefully within the confines of SR. The independent outside observer might be a little rogue.

The magic rogue observer... everyone should have one.

DrGreg, thank you very much for your time.

Wes
...

 

[Wes Tausend]

...People sometimes fool themselves by trying to set $v$ equal to $c$ in the length contraction and time dilation formulas just to see what would happen, and then they come up with conclusions such as your "a peculiar property of light is that it takes no time at all from source to destination". The problem is that the derivation of the formulas depends on there not being any frame in which the speed of light is not $c$, so setting $v=c$ invalidates the results.

Not so... For any observer, anywhere, the time it takes for light to get from source to destination is the distance between the source and destination, divided by the speed of light.

Nugatory,

I pretty much agree with what you say.

Thanks for taking time to further explain standard constraints and pitfalls. I've waited so many years to ask about assigning light to a rest frame in a thought experiment, I've become an old man. I'm afraid minds do expire a bit after retirement age, but better late than never.

The following may still be wrong, but I think I very much inadvertently mis-worded my statement, "But a peculiar property of light is that it takes no time at all from source to destination." I think I should have stated, "But a peculiar property of light is that, in it's own reference frame, it takes no time at all from source to destination." I've seen the phrase used before and assume that it means that, at the speed of light, time stands still. Therefore under these conditions, it seems light departs and arrives at the same time (instantly) within it's own frame.

I'm sorry this deviation of SR doesn't work out so well. If the imaginary visualization model made it through SR, my next area of question would have been a similar mental exercise in GR. In this imaginary case, to an outside observer, the "matter explosion" mentioned above to DrGreg, must continuously ever so slightly accelerate if we are to visually include the accelerated sensation of simple gravity throughout the universe. As a mirror image example, gravity would simply be imagined to be a constant all-atomic repulsion, and subsequent inertial reaction of adjacent mass, rather than constant all-atomic attraction. Unfortunately, for all my effort to gain visual insight, the enigmatic root origin of any type gravitational force remains mysterious to me.

The only possible visualization advantage I can imagine is, mirrored, expansive gravity seems to travel in the same direction as the Big Bang (or perhaps "steady little banging"). One can imagine that the continued force of that historic event might cause a permanent sensation and behavior of constant "gravitational" acceleration. I can also imagine this coincidence to measure (by exploding ruler?) similar, if not identical to Einsteins traditional gravity. In a way, this "alternate gravity" seems more identical to common acceleration to me than traditional GR. Frankly, a mirror image of anything should logically appear simultaneous and identical within the laws of physics... except left to right.

That no one else has seemed to previously grasp and use my mirror image tool, does cast a dark shadow over my ever finding my "backwards visualization" worthy of insight. Not only that, but it encourages my fear that I am not only out of the box, but outside the fence of physicforums rules. I understand that if a "unusual perspective" cannot be contained within standard SR (and therefore GR), it possibly cannot be discussed here. I fear whether the exact mirror image is close enough to SR to make an exception, or is resolving this particular idea in our physicsforums entirely untenable?

My intent was to reduce difficult-to-visualize Relativity "epicycles" (similar to heliocentricity vs geocentricity), but I may have added epicycles if no one can legitimately gain an improved perspective of comprehension. If this visualization must unfortunately be an entirely separate theory, I see this mirror image as the only possible alternative to Einsteins Relativity. But that will certainly sink me here. Does any reader at all see any merit to continue pursuit of this idea on another, less stringent forum?

Thanks again, Nugatory.

Wes
...

 

[TumblingDice]

The following may still be wrong, but I think I very much inadvertently mis-worded my statement, "But a peculiar property of light is that it takes no time at all from source to destination." I think I should have stated, "But a peculiar property of light is that, in it's own reference frame, it takes no time at all from source to destination." I've seen the phrase used before and assume that it means that, at the speed of light, time stands still. Therefore under these conditions, it seems light departs and arrives at the same time (instantly) within it's own frame.

The concept of a reference frame doesn't apply to light, as it is never 'at rest' in any reference frame. This applies to all massless particles which always travel at the speed of light.

I just read another well-written tip from Nugatory a moment ago - it fits perfectly here, too.:

Massless particles don't have a frame of reference at all.

One thing that may be confusing you here is our bad habit of talking about "the frame of reference of <something>". Frames don't belong to objects, objects don't own frames, so strictly speaking we shouldn't be using the word "of" here to suggest that the object has its own reference frame. When you see the words "the frame of reference of <something>", you should read that as convenient shorthand for the more precise "a frame in which <something> is at rest". There are no frames in which a massless particle is at rest.

 

[Doc Al]

Thread closed for moderation.