Probably an elementary relativity question but,
From the relative perspective of a particle moving at the speed of light, is distance a constant?
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Probably an elementary relativity question but,
From the relative perspective of a particle moving at the speed of light, is distance a constant?
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It is not clear what you are asking, but as long as the speed of a particle remains constant and thereby inertial without any acceleration applied, distances will remain constant in the particle's frame also, yes, although different to what would be measured in other frames of reference for speeds under c.Originally Posted by uncommonsense
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The distance beween two points in frame F is d.
According to special relativity an observer moving at speed v wrt frame F measures the distance between the two points to be d'=d*sqrt(1-(v/c)^2).
This is the so-called "length contraction". To answer your question, make v=c.
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It's hard to imagine, but yes, I was referring to a particle that has obtained c. Difficult to understand because at that instant, all places in the universe are at an equal distance from the particle - as if the particle was, relatively, at the center of a universe where all points in the universe were located on the surface of a spherical shell and the particle was at the exact center of the sphere. The particle can "move" to all places with same "effort". So then, how does it "choose" where to go?
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Consider it from our point of view of a ship that travels away at c. The time that passes for the clocks and passengers on the ship has frozen from our perspective, so they are in stasis as far as we are concerned, and we can see that the ship can travel from point A to point B in some time on our own clock, but no time has passed for the clocks and passengers on the ship, so from their perspective they have travelled instantly. Since the relative speed cannot be greater than c to the passengers of the ship either, so cannot be infinite, then the distance measured to have been travelled is zero also from the perspective of the ship observers, whereas zero distance divided by zero time is any real value for the speed, which is c in this case. SR puts things in a better perspective for speeds under c, though, rather than working through infinities, so it is best when actually attempting to do thought experiments and work through the math to use some speed that is perhaps close but still less than c.
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Thank you. I guess i'm hung up on what happens from the perspective of any particle reaching c. It seems that any consideration of a particle going speed of c leads to imagining that the particle, from it's perspective, is no longer moving, as distance is a constant and time is 0, and so the particle is at all places at once, as is the universe. Have I imagined too far out?
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One might also wonder how time can pass for us as a particle such as a photon travels from point A to point B when from the particle's perspective, our clocks are also frozen. A photon sees all clocks always frozen at the same time they were when the photon was emitted at c, but due to the relativity of simultaneity, observers still say it took some time for the photon to travel from one position to another. For instance, using speeds just under c for better clarity, all passengers on a train will say that all of their clocks are synchronized, but an observer standing on a platform watching the train whip by at near c will say that their clocks are simultaneity shifted to greater times for the readings on the clocks at the back of the train and lesser times on the clocks at the front of the train, although due to the relative speed, the platform observer will say that all of the clocks are barely ticking at all, pretty much frozen. But although the clocks are frozen and the platform observer considers himself to be standing still, as the train goes by each clock he reads on the train directly in front of him will read a greater time as the train passes due to the relativity of simultaneity for the readings on the clocks along the length of the train. So to the passengers on the train, it is the platform observer's time that is nearly frozen, but their own clocks will read greater and greater times as each clock passes the platform observer directly, same as the platform observer observed directly for the clocks that coincided in front of him as the train passed, but to the passengers, time is passing normally as the clocks in the back read a greater time when they see the platform observer pass than the clocks in the front when the platform observer passed those.
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Everybody wonders about the perception of a photon eventually, but one has to be very careful when working directly with infinities in this way, since it is very easy to get caught up, so the best way to go about it is to work with some speed that is just under c to help visualize what is taking place and then slowly push it toward the limit.
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That is not quite right.
Length contraction occurs only along the axis of motion. Distances along an axis transverse to velocity vector are unchanged. That is all part of the Lorentz transformation.
It is important to look at the complete group of Lorentz transformations and see what they imply. The elementary description in terms of length contractions and time dilations can become quite confusing unless you are used to them.
The bottom line is that applying the Lorentz transformations to the "reference frame of a photon" results in singularities because of terms that then have a zero denominator. The reference frame of a photon is not an acceptable inertial reference frame.
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Thank you. I can grasp relativity of simulaneity. It makes sense.
I am trying to self study relativity but I can't quite grasp the distance issues I mentioned above. Most discussions and explanations on relativity center upon time. Time is a rate. Obviously, f a rate is relative it is due to the relativity of its components - so I am looking closer at distance and space(kinda synonymous).
If we accept that a particle can reach c, then we must understand how that particle deals with a universe with all points in space at a single place, and therefore time is 0, or the other way around, any thoughts?
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DrRocket answered that one well in the last post. From the perspective of the photon, the universe is a flat plane, so still exists in two dimensions.
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That make sense, but now I am imagining that the particle experiences O timke and distance, and space for that matter, only along one axis, and so it now exists in a 2 dimentional universe???
ETA I was posting at same time as last response
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Thank you. Excellent responses. I am fascinated.....
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You are trying to impose the prejudices of everyday experience and language on special relativity. That is not only difficult and confusing, it misses the major point of Einstein's theory, and that is that you must deal not with space and time but with a merger of the two - space time.
One observer's time is to another observer a mixture of both space and time. You cannot cleanly separate space from time, except in the reference frame of a single observer. General relativity tells us that you cannot separate them even for a single observer, except as a local approximation.
Special relativity is the local approximation to general relativity.
All of this requires some detailed study of the Lorentz group, the group of linear transformations that preserves the Minkowski metric or quadratic form. There is a nice treatment of this subject in the book The Geometry of Minkowski Space time by Gregory Naber.
In a good treatment of the geometry of special relativity you will find an invariant treatment of the transformations and see the subtle way in which space and time are woven together in a single entity. It helps to overcome the confusion that arises from looking at "time dilation" and "length contraction" alone. They are merely coordinate effects that come from what is really preserved, the Lorentzian length of an interval.
One sign of confusion is the problem that you are having with a photon. You simply cannot apply the transformations in the frame of a photon, for there is no such thing. No experiment can be performed, even in principle, in such a frame. The theory does not address it either, as the transformations would be singular/undefined.
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Only particles of 0 rest mass can reach c, and they cannot travel at any other speed.
You do not have to understand how that particle deals with the universe. The theory does not address that issue. It predicts the outcome of experiments conducted in reference frames in which experiments can be conducted.
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uncommonsense,
Distances at c
Probably an elementary relativity question but, from the relative perspective of a particle moving at the speed of light, is distance a constant?Maybe by your last response your question has been answered. Thought I'd mention a couple of points. Using the word particle implies that the entity has mass. however you could mean particle of light meaning a photon.Thank you. Excellent responses. I am fascinated.....
If you are talking about atomic particles, or other massive particles, to continue traveling at close to the speed of light the particle would need continuous acceleration (see correction below). As to distance, according to the BB model, distance in the past and present has the same measure regardless of the perspective of matter moving through it so that distances would remain constant regardless of the motion or perspective of mass within it. Accordingly, if a particle is traveling at a "constant speed" considering both length contraction and time dilation, the distance traveled per unit of time would accordingly remain constant from any single SR perspective, regardless of any constant speed.
Last edited by forrest noble; 2010-Mar-17 at 05:02 AM. Reason: correction noted Dr. Rocket; shb continuous force to maintain its velocity
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Umm don't think this is right. If you go by the reference frame of the object travelling at c then the universe collapses in the direction of motion to 0 length, Time stops for said object and in essence would then be in a 2D universe. For the particle to move to a point perpendicular to its direction of travel it would have to accelerate in that direction.
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No
Acceleration is a change in velocity. A particle traveling at a fixed speed in a straight line (a fixed direction) does not accelerate.
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Dr. Rocket,
Thanks; I meant force and velocity (not acceleration); a continuous force to maintain speed/velocity.
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I'm getting alot of great information. Another question based upon prior answers: If travel along single axis at c eliminates the experience of that dimention for the traveler, does light "bending" around a planet/sun (whatever), thereby moving on a 2 dimentional path at speed of c, result in the light experiencing the universe in only 1 dimention?
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Careful, this has been discovered experimentally not to be the case. See here
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uncommonsense,
Light traveling past a star or galaxy will bend toward that gravitational influence in a curve within a single plane from a single axis. If the center of gravity of the object changes over the path, such as when traversing or passing by a galaxy, the curve can become multi-plainer, multi-axial, and 3 dimensional over its course.If travel along single axis at c eliminates the experience of that dimention for the traveler, does light "bending" around a planet/sun (whatever), thereby moving on a 2 dimentional path at speed of c, result in the light experiencing the universe in only 1 dimention?
As the light passes close to any star it would probably change its previous plainer course.
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That seems like quite an assertion when the article you linked to makes no mention of rest mass. Exactly the term DrRocket used.
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I don't disagree that space time is at the center of most relativity discussions, and that the major point is merger of space and time.
But, time has no inherrent aspects -rather, it is a rate that compares the movement of one thing thru space to the movement of another. It compares distances. Thats it. So I find it clearer to imagine the merger of movement and distance. Maybe I shouldn't.
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You need to understand the article first, comment after. For people knowing physics, the article is quite clear.
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This may be at the root of your problem. You're thinking of time classically, as something separate from space. In spacetime, a change in time is a movement through spacetime. Each event in spacetime requires four coordinates, three space, one time. As the time coordinate of a partcle changes, that particle has moved through spacetime. It matters not whether the space coordinates have changed.
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??
The link simply says that if neutrinos have 0 rest mass then they travel at c and if they have positive rest mass (which they apparently do according to recent experiment) then they travel at less than c. That is no contradiction.
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No, because if you have force then you have acceleration. Force will change the speed unless it is applied normal to the velocity in which case it merely changes direction (as in circular motion).
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That article in no way contradicts what DrRocket said. Clearly, the issue in that article is simply that speed can never be accurately enough measured to determine whether or not any given particle has zero rest mass, whenever the rest mass is on the scale of tens of MeV or less. Nevertheless, we expect a particle to require exactly zero rest mass to move at exactly c in a perfect vacuum. As none of those three things are ever establishable in practice, we will always have uncertainties in practice that are nevertheless not built into our best theory, the latter being what DrRocket was commenting on.
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Let's go back to this, because I think this is the source of your problem. This question is fundamentally inconsistent with itself, and not because of the reference to c-- rather, because of the use of the "relative perspective of a particle" being used along with the word "moving." That's inconsistent, right there. As soon as you talk about the relative perspective of a particle, it is part of that perspective that the particle is not moving. So a moving particle has no relative perspective, it's meaningless-- only stationary particles have "relative perspectives."
So what are you really asking? You are asking about the perspective of a particle that is stationary, that perceives a bunch of other things that are moving, and asking to make a comparison between that particle's perspective, and the perspective of some other moving particle (in the latter particle's frame, where it is of course stationary). So you are asking to compare the frames of reference of two particles, each stationary in their own perspective, but in relative motion-- where the relative motion is c. That situation must exhibit reciprocity, meaning that you cannot tell from the answer to the question which one is "really moving"-- so if one particle sees "contracted space", then so does the other.
This can get confusing. The first problem you face here has been pointed out-- the singularity of c. So don't start with a relative motion of c, use some v very close to c, and just take the limit as v goes to c. Will anything unusual happen during that limiting process? No, it's all the same, at every step along the way, so the limit is not particularly insightful and it is really the steps that tell you what you want to know.
Consider again the reciprocity. Let's imagine two particles approaching each other at some v very close to c, and imagine a football field with lines on it that is at the intermediate speed, meaning that in the frame of the football field, both particles appear to be moving at the same speed. That speed is not v/2, it will be close to c. But more to the point, both particles will see the lines on the football field to be highly contracted in the direction the field is moving, and both will think that is happening not because the particle is moving (it isn't in that perspective), but because the field itself is moving.
So if we have a particle that sees everything in the universe as moving in a single direction at a speed very close to c, then distances between the moving stuff in that universe will be contracted, but not because the observer is moving, but because the stuff in that universe is moving. In other words, that observer may conceptualize a perfectly stationary universe in which distances are not contracted in any way, but within that stationary universe is a bunch of moving stuff, and the moving stuff is very contracted in the direction of motion, because of its motion.
So what about the limit as the motion goes to c? The stuff just gets more contracted, if there is a finite amount of it (if there is an infinite amount, there continues to be an infinite amount, covering an infinite distance at all stages of the limit). So if there is a finite amount of stuff observed, it gets contracted to a very thin shell as v goes to c, but it's all seen as a consequence of the fact that the stuff is moving-- there could also be some stuff perceived as not moving that would not be contracted at all. So it really isn't true that the universe itself contracts for particles that are moving near c relative to us-- all we can say is that the stuff we see in the universe that we don't see as moving all that fast would appear to have a highly compressed density to that other observer, but it would be a manifestation of the motion of the stuff-- that observer would be living in a universe where the stuff in the universe (not the space or time of the universe) would have a curious property of moving very fast and being very contracted. There could still be other stuff that neither. Such an observer would say think "how curious that I'm moving so fast the universe has a bunch of really contracted stuff in it", such an observer would just think "I wonder why that huge amount of superdense stuff is moving so fast that it is so highly contracted relative to the rather low average density that it perceives itself has having?"
And all this is special relativity language-- when talking about the "universe" that we now perceive, one would really have to be using GR language, and I have no idea what that would sound like to an observer moving relative to us at speeds closer and closer to c.
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