Riding on a beam of light - time and space

  1. something is confusing to me. lets say i am in an inertial unaccellerated frame, at some sort of relativistic speed. and lets take another inertial frame, an observer on earth.

    here is what i have read. the observer on earth measures the relativistic frame's ruler as being less than his own, and measures the relativistic frame's clock ticking slower than his own.

    but this is also true of the relativistic frame, measuring the ruler and clock of the earth observer's frame as being smaller and ticking more slowly than his relativistic frame's ruler and clock.

    i have read that if one was travelling on a beam of light, that one would measure no elapse of time and no distance covered, no matter how far the observer on earth measured the light beam to go. but if the guy on the light beam measures no time elapsed and no distance travelled, how could he at the same time, measure the earth observer's clock to be going more slowly than his own, which has measured no time at all ? ditto for distance.
     
  2. jcsd
  3. ok.Now when the observer is on the light beam,he would see that the earth is moving past him at the speed of light.Therefore,in his frame the earth's clock would not tick.THat is the time dilation from his view for earth would be infinite.
     
  4. disregardthat

    disregardthat 1,841
    Science Advisor

    How can the observer on the light beam see the earth move at the speed of light, when time dialated for him is infinite? For the beam it would take 0 seconds to travel from A to B. Of course it is physically impossible to observe from a beam of light.
     
  5. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Time does not exist for a photon, since it is travelling at the speed of light, and so it makes no sense to discuss how fast the photon sees the observer's clock to be moving.
     
  6. one sees this situation mentioned all the time (riding on a light beam).

    so, if time does not exist for a photon, does space exist ? according to the argument, the observer on the light beam registers no distance travelled.

    lets also take a look at another example - instead of being on a light beam, one is travelling close to the speed of light. he notes that the ruler on earth is very small, and the clock on the earth is moving very slowly. what do his rulers and clocks mention ?

    what seems to be inconsistent with me is that as you go faster, you measure the other guy's ruler as smaller and his time ticking slower - but your ruler and clock does not change. just like the guy on earth - his ruler and clock havent changed to him. he sees the guy travelling very fast as having changed.

    so if there is no time for a photon, then up to the smallest increment less than the speed of light, one measures his own rulers and clocks as being normal. and then somehow it disappears altogether if it could reach the speed of light ?
     
  7. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    A photon knows no concept of distance.

    By his "rulers and clocks" you mean his proper time and proper distance. The proper time and proper distance for an observer are always the same, no matter how fast he travels (<c)
    Well, the major problem with this is that you are assuming that an observer can be accelerated to the speed of light. However, this is not true! An observer with a nonzero mass can never travel at the speed of light, and thus the situation where the proper time and proper distance cease to exist can never happen.
     
  8. okay, so in your opinion, a photon has no concept of space or time. but this must occur only when the photon is travelling at the speed of light. this occurs in a vacuum. the photon does not always travel at that speed. physics tells us that it slows down in other mediums. so obviously, we must be talking not so much about the photon, but rather "travelling at the speed of light".

    i understand that according to einstein, nothing can be accellerated to that speed.

    yes, i am talking about his proper time.

    it does seem strange to me that up to the most minute fraction below that speed, an inertial frame measures his own clocks and rulers as not having changed, but at the speed of light - there are no rulers or clocks at all.
     
  9. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    This isn't my opinion; it's what the theory says!
    Please see here for a discussion on the issue of the speed of light decreasing in a medium.
     
    Last edited: Feb 20, 2007
  10. JesseM

    JesseM 8,491
    Science Advisor

    It is impossible to define a "rest frame" for something traveling at the speed of light (in a vacuum) without violating the postulate of relativity which says the laws of physics should work the same way in all inertial reference frames (and you also get nonsense answers if you plug c into the 'Lorentz transformation' which transforms between the coordinate systems of different frames in motion with respect to one another). If you're interested, there was a long discussion of this issue on this thread. But it might help to think about what happens in the limit as your speed relative to the galaxy (or some other convenient landmark) approaches c. In this limit, you will measure the galaxy's length in the direction you're traveling to approach zero, so the time it takes on your clock to move from one end to the other approaches zero too, which is consistent with the galaxy's perspective where your clock approaches being frozen in the limit as you approach c. But another important issue has to do with the relativity of simultaneity, which refers to the fact that clocks synchronized in one reference frame will be measured to be out-of-sync in another frame, and this out-of-sync effect will get larger as the relative velocity increases. In the galaxy's frame, its own length is around 100,000 light years, so in the limit as you approach c the time you are measured to cross it will approach 100,000 years. If there are clocks on either end of the galaxy which are synchronized in the galaxy's frame, then by the time you pass the second clock, its date will be about 100,000 years beyond what the date was on the first clock as you passed it. However, in your frame both clocks are ticking slower than yours (in the limit both clocks will approach being frozen in your frame), and you pass the second almost immediately after passing the first (in the limit, the time between these events approaches zero); the only reason the second clock reads a much higher time is that it was out-of-sync with the first by about 100,000 years to begin with in your frame.

    By the way, on an older thread I came up with an illustration of how the difference in simultaneity insures that two rulers and clocks moving at a significant fraction of c could each see the other one shrunk and each see the other's clocks ticking slow without it leading to a physical contradiction--that's here if you want to look at it.
     
  11. hi cristo,

    i read the discussion. while it seems plausible, i hope it is meant as a possibility, and not a sure thing.

    i have read that the guy on the light beam measures no distance or time, but not that distance and time do not exist. that is not to say that i dont believe that the theory says this - just that i have not interpreted them to say that.

    i guess what i find lacking about the 2 theories on relativity is that they give us explanantions about our measurements, but they dont have anything to do with the actual reality of what is, since every frame of reference comes up with different answers.

    all these frames come up with the speed of light being the same.

    i think the main problem we have is that we cant get measurements instantaneously. and when objects are moving at near the speed at which we can receive information, it really skews our perception of reality, whatever that may be.

    i am beginning to think that the arguments about time not being a real thing, but simply being a result of motion - is becoming more likely.
     
    Last edited: Feb 20, 2007
  12. thanks jesse,

    i will read them later, when i have more time.
     
  13. JesseM

    JesseM 8,491
    Science Advisor

    But there is no "guy on a light beam", it's a meaningless idea according to modern physics. Einstein did imagine this as a thought-experiment, but it was a sort of reductio ad absurdum of the old pre-relativistic concept of electromagnetism which would allow things like this.
    There are many invariant quantities which would be agreed on by all reference frames, like the "proper time" between two events along a given object's worldline, or the invariant space-time interval between two events in special relativity. But more to the point, why do you think that there must be a single "actual reality of what is" for quantities which depend on your reference frame in relativity? As a comparison, in Newtonian physics different reference frames will disagree on the velocity of a given object--do you think that every object must have a single absolute velocity? Likewise, different spatial coordinate systems will disagree on the x-coordinate of a given object in space--do you think every object must have a single "objective" x-coordinate, based on a single "objective" set of coordinate axes?
    Not sure what you mean by this. You can have all measurements be made locally, by rulers and clocks that are right next to the event as it happens, so there is no delay between when the event occurs and when it is measured. Of course if measurements are made at different locations it will take time for signals about the results to reach you, but the information doesn't change as it travels, you could imagine each local measuring device sending me an email about what it found and obviously the email's text won't change between when it was sent and when it reaches me.
    Unless you can specify the experimental consequences of time being a "real thing" vs. being the "result of motion", this is just some sort of philosophical question (and philosophers might not even consider it well-defined), not a physical one.
     
  14. hi jesse,

    i wanted to reply to this statement now. isnt this a bit of circular logic ? i understand that these quantities vary in the theory of relativity.

    but the theory of relativity does not give us answers as to "what is", only as to "what i measure them to be".

    if one has 2 answers, then both answers can only be right in its inertial frame. the object itself does not actually exists in 2 different places at the same time.

    it is not that i am disagreeing with the theories of relativity - just that they do not explain to me what the universe is - they merely give me predictions based on my measurements.

    just as in your example about the galaxy shrinking to zero in the direction of my motion. the galaxy did not actually shrink. it only seemed to do so, based upon the fact that i am travelling very fast, and my measurements tell me that it shrank.

    i do think there is an absoluteness to reality. i suspect that we will never be able to figure out what reality actually is - only what we perceive it to be.
     
  15. light/info has a max speed of c. some light that is reaching us today comes from events that happened billions of years ago. we can not get information instantaneously. if we could, i believe we would all see one reality, instead of a zillion different perspectives.
     
  16. JesseM

    JesseM 8,491
    Science Advisor

    Yes, but the symmetry between reference frames is very fundamental, it would be strange if it were violated by "what is" even though the laws of nature are so scrupulous about obeying this symmetry for what is measured.
    How do different reference frames imply the object "actually exists in 2 different places"? Certainly an event can be assigned different coordinates by different frames, but that's true in plain old Newtonian physics as well. You didn't answer my question about velocities and spatial coordinates--do you think there must be a single "true" answer to what an object's velocity is, or what an object's x-coordinate is (implying that there must be a single "true" answer to where the origin of the x, y, z axes lies)? Even if we ignore relativity, there is no objective answer to these questions even in Newtonian physics. Couldn't it just be that coordinate systems are human inventions and that there doesn't need to be an objective answer about coordinate-dependent quantities?
    No one is saying the galaxy "actually shrank", it's just that all measurements of length depend on your coordinate system. The only objective facts might be facts about pairs of events which happen in the same local region of space and time--if I say that I measure the galaxy to be 1 meter long, all that really means is that the left end of my meter-stick was passing next to the left end of the galaxy "at the same time" (in my coordinate system) that the right end of my meter-stick was passing next to the right end of the galaxy. And I define "at the same time" in terms of synchronized clocks at either end of my meter-stick...for example, perhaps at the moment the left end of my meter-stick was passing the left end of the galaxy, a clock mounted at the left end of my meter-stick read 3:00, and at the moment the right end of my meter-stick was passing the right end of the galaxy, a clock mounted at the right end of my meter-stick read 3:00. Now, all frames will agree that both these local events occurred in the same way--they all agree that at the moment the left end of my ruler passed the left end of the galaxy, the clock on the left end of my ruler read 3:00, and same with the right end and the right clock. It's just that they define "synchronized" differently in their own coordinate system. For example, there might be two additional clocks at rest relative to the galaxy sitting on the left and right end of the galaxy, and "synchronized" in the galaxy's frame rather than my frame. In this case, all frames would agree that the following three events happened in the same local region of space and time:

    -my ruler's left end passing next to galaxy's left end
    -my clock sitting on left end of my ruler reads 3:00 PM, Jan 1, 2000 AD
    -galaxy's clock sitting on left end of galaxy reads 3:00 PM, Jan 1, 2000 AD

    And likewise, all frames would agree these three events all happened right next to each other in space and time:

    -my ruler's right end passing next to galaxy's right end
    -my clock sitting on right end of my ruler reads 3:00 PM, Jan 1, 2000 AD
    -galaxy's clock stting on right end of galaxy reads 3:00 PM, Jan 1, 102000 AD

    In my frame, the left end measurement happened simultaneously with the right end measurement, so in my coordinate system that means the galaxy is 1 meter long. But in the galaxy's frame, the right end measurement happened 100,000 years after the left end measurement, so it doesn't have anything to do with the length of the galaxy, it just means the ruler has had time to cover a very large distance between these two events.

    So the question is, why do you think there has to be any "real truth" about whether different events which do not occur in the same local region of space and time happened "simultaneously" or not? Why can't simultaneity be entirely coordinate-dependent, just like most people would assume an object's x-coordinate depends on where you happen to choose to place the origin of your xyz coordinate axes, and what direction you choose to orient the axes? Unless you think there must be an "objective truth" about whether two objects share the same x-coordinate, I don't see why you'd find it necessary to believe there must be an objective truth about whether two events happened at the same time-coordinate. We can just say there's an objective truth about which events happened next to each other in the same local region and leave it at that?
    So do I, I just don't think there's an absolute truth corresponding to every coordinate-dependent quantity. If I draw a dot on a piece of paper, do you think there's an absolute truth about whether this dot lies at x-coordinate x=5 cm or x=2 cm, when either could be correct depending on where I choose to position the origin of my x-axis? Do you think there is some objective truth about where the origin of the x-axis "really" is on a piece of paper, even before I choose where to draw an x-axis?
    But again, all events can in principle be measured locally. If I am standing on the left end of a ruler that's 1 light year-long while my friend is standing on the right end, and we each are carrying clocks which are synchronized in the ruler's rest frame, then if an event happens on the right end, my friend can measure the position and time of the event right when it happens and then send this info in an email to me. It's true that the email will take 1 year to reach me, but it's not as if the text of the email is somehow going to change on the journey to me.
     
    Last edited: Feb 20, 2007
  17. hi jesse,

    thanks for the very long post. i have no problem with your x being 2 and mine being 4. but when we both measure the size of something and come up with different answers, both of them are not correct.

    i am interested in what is, not what we perceive things to be.

    we can only imagine in 3 dimensions. so lets think about an expanding ball. the surface area is an ever expanding 2 dimensional sphere. everyone on that sphere sees himself in the middle of the sphere, when in reality, the middle of the sphere does not even exist in their universe, since the middle is the core, and they are on the surface.

    however, they are all discussing 2-dimensional relativity, and how each of them sees things as they move along the sphere.

    but us smart 3 dimensional beings can view the entire sphere at once, and understand its true reality.

    i suspect that we are part of a real 4th dimension, something other than time. and we have no more ability to understand our 3-dimensional reality any more than the people on the sphere have of understanding their universe like we do.

    the only difference is that i dont think most scientists today understand this.
     
  18. when i say "sphere", i should have said surface area on the sphere, as sphere is usually thought of as a ball.
     
  19. JesseM

    JesseM 8,491
    Science Advisor

    But why do you think size is different from x-coordinate in this way? I would say that measuring the length of something intrinsically depends on having a definition of simultaneity--if I say a moving object is 1 meter long, it's because the back end of the object was passing next to the back end of my meter-stick "at the same time" as the front end of the object was passing next to the front end of my meter-stick. If you are willing to consider the possibility that the question of whether two events happened at the same t-coordinate might be just as subjective and coordinate-dependent as the question of whether dots on a piece of paper have the same x-coordinate, then I don't see how you can escape the conclusion that length is subjective and coordinate-dependent as well. Can you think of a notion of length that is not bound to one's definition of simultaneity?
    And what makes you so sure that length is part of "what is"? Consider a bunch of cylinders in 3-dimensional euclidean space, with no time dimension. Even if we both choose a different set of xyz axes, we will both agree on the distance between any two points in this space, like dots drawn on the surface of different cylinders, when we calculate this distance according to the pythagorean theorem [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}[/tex] in terms of our own respective coordinate systems (with one dot having coordinates [tex](x_1, y_1, z_1)[/tex] and the other dot having coordinates [tex](x_2, y_2, z_2)[/tex]). However, we will not necessarily agree on the diameter of the ellipse formed by taking a cross-section of the tube in the xy plane, since our xy planes may be oriented at different angles.

    Similarly, if we have a 4D minkowski spacetime with different 4D tubes corresponding to the worldlines of objects in this spacetime, and we both choose a different set of xyzt axes, we will both agree on the spacetime interval between any two events when we calculate [tex]c^2*(t_2 - t_1)^2 - (x_2 - x_1)^2 - (y_2 - y_1)^2 - (z_2 - z_1)^2[/tex] in terms of our own coordinate system. However, when we talk about the spatial "length" of an object, we are really talking about the size of the cross-section of one of the 4D tubes in our own 3D xyz plane, and since our xyz planes are oriented differently we'll get different answers. Why do you think there should be an "objective truth" about the 3D cross-sectional area of 4D tubes in 4D spacetime, when you presumably don't think there is an objective truth about the 2D cross-sectional area of 3D tubes in ordinary 3-dimensional euclidean space?
     
  20. hi jesse,

    i tried multi-quote, but it didnt do anything for me. i was hoping it was a layout such that i could reply to your different paragraphs to me.

    i think you may have misunderstood me. i am not saying that i disagree with the fact that different reference frames get different measurements.

    in one of our previous posts, i was attempting to say that our lack of simultaneity is why we perceive the universe as we do, instead of my example of the 3-dimensional being having immediate access to the total sphere, while the flatlanders only have access to a surface area, and not all at once.

    so i am not doubting that different frames have different time and length measurements.

    but what i am saying is that i do believe in one absolute entity. i dont think time is a part of that entity. in fact, it is what screws us up. because it takes time for us to get information. it is not there instantaneously.

    and in a previous post i made a comment about time not being real, but just a part of motion. by that i meant that there would be no time, if there was no motion. time is simply something that occurs because we compare motions of objects of matter.

    that seems to get more likely when i see that time seems to change based upon our velocity, and then apparently disappears altogether when we reach C. this is a humongous red-light clue for someone to discover.

    so while spacetime may make sense as a tool in helping us explain our perceived reality, i do not think of it as a real 4 dimensional thing. and i think we could completely get rid of it entirely if we had information instantly instead of having to wait for it to get to us.

    but i do believe in an absolute 3-dimensional space. and i suspect that it is part of a real 4-dimensional thing of which we will never have any notion about. and this 3-dimensional space would be absolute and not changing if we got information instantaneously.

    if we had immediate access to everything, then we would all be able to agree on simultaneity.

    newton's theories lasted for 200+ years, and are still valid for most everything that we do. how long will einstein's theories last before we make our next big startling discovery ? who knows ? but that is exactly what i think they are - stepping stones, just like newton's theories.

    but like in my previous example, i suspect that there are aspects of this universe that are totally beyond us, forever. just like the flatlanders - they have absolutely no chance of discovering anything about volume. it is a non-sequitor to them, and always will be.

    i believe we are in that same boat. of course, that does not mean that we stop trying - but i think that we should keep in mind (we, being the scientific community), that it may be very likely that we have certain insurmountable hurdles that can not be solved by getting new technology. they are forever beyond our reach.

    with regards to your cylinders, i think there is a true length. and that is the length that an observer gets when he is at rest with the object, has it in his hands, and measures it. anything else is a perceived length.
     
  21. or a perceived cross-section. again, i take it in my hands, and measure its cross-section. that is its true cross-section.
     
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