Monday, April 05, 2004

Where's Einstein when you need him?

I recently read Brian Greene's The Elegant Universe (a really good introduction to modern physics, by the way, I highly recommend it). But there was one particular problem concerning special relativity which I don't understand: if light/photons don't move through time, then how did they get to the present? Shouldn't they all be frozen in that moment of time when they were formed?

Background: The key idea here is that any object is always moving (relative to some other object, I suppose) through space-time at the speed of light. For objects at rest (e.g. me, relative to my chair), all of that motion is going through the time dimension. However, for moving objects, some of that motion is "spent" on spatial dimensions, and so less remains to go through time. Just like if you travel north-east for 100m, you won't get as far north as if you travelled due north for that distance. I find this analogy quite powerful, because it explains (in a reasonably understandable sort of way) why it is that time slows down as objects approach the speed of light, and also why nothing can ever move through space at faster than lightspeed.

But what about light itself? A photon moves through space at the speed of light, so there is no motion leftover for it to move through the time dimension. Greene explicitly says that photons are no "older" now than they were at the birth of the universe. So how did those photons get into the present, if not by passing through time like everything else?

Some musings: I really haven't got much of a clue, so I'm hoping a more knowledgable reader will be able to enlighten me here. But I'll offer some thoughts anyway...
I'm guessing the problem must be due to me having too much of a naive-absolutist conception of space and time. Perhaps the apparent paradox can be solved by expressing space and time in purely relational terms.

I can't yet see how that helps, but to get a feel for it, let's consider the constancy of the speed of light:
If two cars, each travelling at 50 km/h (relative to an observer sitting on the footpath) are travelling in the same direction, then they are stationary relative to each other. If moving in opposite directions (e.g. about to have a head-on collision), then their relative speed is 100 km/h. All nice Newtonian stuff so far. But light is different. No matter how fast you're moving, in whatever direction, photons are always travelling at a constant speed c (the speed of light) relative to you (and everything else for that matter).

To apply the 4-d space-time stuff to the above examples:
  • The observer sees all the cars as going at the same speed (50 km/h), so they all move through time at the same rate relative to him (which is very close to full-speed, but not quite).

  • The same-direction cars are relatively stationary, so they move through time at full speed (i.e. slightly quicker than from the observer's perspective).

  • The head-on cars are going relatively fast, so each moves through time relatively slowly (though the difference at this scale, compared to the speed of light, is so tiny as to be indistinguishable to humans).

So "how fast is the car moving?" is a nonsensical question unless you include the frame of reference (i.e. "how fast relative to X..."). Moreover, the car is moving through time at different rates, depending on who the observer is.

So what about photons then? No matter the frame of reference, their speed is always the same: c. So no matter the frame of reference, their movement through time is always the same: zero.

Well, that was no help.
Any ideas... anyone?

Update: see here for the answer.

1 comment:

  1. The answer is trivial, although it's perception is outside the current paradigm of thought. There exists an incorrect "assumption" in fundamental electromagnetic theory.

    For almost 100 years we have assumed that photons physically traverse non-zero distances, i.e. that photons literally move.

    In his second paper of 1905 Einstein wrote:

    "In accordance with the assumption to be
    considered here, the energy of a light
    ray spreading out from a point source is
    not continuously distributed over an
    increasing space but consists of a finite
    number of energy quanta which are localized
    at points in space, which move without
    dividing, and which can only be produced
    and absorbed as complete units."

    This work by Einstein was truly brilliant, and I
    agree with most if it, however, I now disagree with
    his assumption that such energy quanta actually
    (i.e. literally)'move' any distance at all, from the
    point of emission to the point of absorption.

    He actually made _six_ assumptions:

    1) The energy of a light ray spreading out from a point source is not continuously distributed over an increasing space.

    2) The energy of a light ray consists of a finite number of energy quanta.

    3) The energy quanta of a light ray are localized at points in space.

    4) The energy quanta of a light ray move without dividing.

    5) The energy quanta of a light ray are absorbed in complete units.

    6) The energy quanta of a light ray are produced in complete units.

    Initially this paper paper, he assumed that a light ray’s energy quanta “move without dividing”. There was no evidence for such, this was simple limited deductive reasoning of how a particle, namely the ‘energy quanta’ of a light ray produced at source A came to exist at point B. Einstein used real motion (i.e. the human perception of locomotion) on this _new_ particle he conceived.

    Considering that most of mainstream science considered “light to travel through manifestly empty space”, his assumption was imprisoned by human perception. Concerning particles as previously defined particles (i.e. bits of matter with real mass) have been considered, real motion from A to B was his only option.

    The photons motion is relative! I'm simply adding one more degree to Einstein's relativity and one degree of discountinuity quantum theory.

    The energy quanta of electromagnetic radiation
    do not physically ‘move’ any distance (at all),
    as EM waves propagate from the point of emission
    to the point of absorption.

    This means that photons are manifested one at a time, in succession from the point of emission to the point of absorption. Just as in Maxwell's third and fourth equations, a changing magnetic field manifests a changing electric field and vice-versa.
    The rate at which photons are manifested is very
    specific in any isotropic medium.

    Once grasping this many of the unexplanable phenomena are easily explaned.

    For example, the speed of light MUST be constant regardless of the motion of source or target.

    Particle/wave duality is explained, because EM radiation is at ALL times a propagting wave of non-moving particles.

    Photons exist as part of an EM wave. They exist in
    our realm for a very very brief moment.

    Now to address your comments:

    > So what about photons then? No matter the
    > frame of reference, their speed is always the
    > same: c.

    No! The photon speed is ZERO.
    The EM wave is propagted at c, which
    is the rate at which non-moving photons
    are manifested.

    > So no matter the frame of reference,
    > their movement through time is always
    > the same: zero.

    They do not MOVE through time at all. For
    a very brief moment the photon will exist in our
    time, i.e. they will have real and defined values for ENERGY, LOCATION, and TIME.

    Kind Regards
    Don Palermo


    Posted by Don Palermo


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