Relativity Discussion Forum

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Most physicists and philosophers seem to be confused about the notions of time and space because they try to imagine them as entities which have an independent physical existence. This is obviously not possible because we ourselves are objects within space and time. The latter can therefore only be treated as indirect qualities of the physical world: the spatial dimension allows objects to exist physically in the first place and the temporal dimension allows for changes (e.g. movement). The time-units used to describe any changes quantitatively are of course only a matter of convention (e.g. through astronomical or atomic standards, or simply a clock ). By definition units should be invariant and the concept of flexible spatial and temporal units, as proposed by Einstein, is therefore a contradiction in terms.
As long as a time-standard is physically stable (i.e. not subject to deterioration or mechanical or other forces) all events are therefore uniquely determined on the time scale. If observations show a change in the time scale of a given event, then this has, as a matter of principle, to be explained as a physical mechanism but not as change of the measuring time-unit.

The 'moving-train' thought-experiment is flawed for two reasons (as explained on my website (under Special Relativity)) : a) it actually contradicts the invariance of the velocity of light and b) it takes the peculiar properties of light propagation as a reference for defining the movement of material bodies (it is obvious that time- and space- units can well be defined without the involvement of light at all).

As 'time' manifests itself only through changes in the physical world, speculations concerning its underlying nature really do not make any sense and will in fact lead to inconsistent conclusions in any physical theory. There is one thing one can say however: contrary to the suggestions of science-fiction authors and even some physicists, time can obviously only go forwards, as it is given by the impression of change as such but not the way or direction of these changes (one could construct a clock that runs backwards, but the fact that it runs at all would still mean that time goes forwards). You would have to put yourself outside space and time in order to manipulate them, but this is obviously not possible.

Most physicists will probably point out that Relativity is well supported by experiments but it is clear that a theory which is internally inconsistent can not be subject to experimental verification or falsification.

Christopher (2)
thank you ... i think you & i may be seeing the same world ...

i sat down one day (a year ago ) to think about " the psychology of time " ... i had never thought about time before , but i had a few days free ... and i thought it might be interesting to investigate it ... a few hours later i realized some_thing ... " time does not exist. all there is is the ever_changing now. "

let me explain myself ...

space exists. and space changes shape. we remember the shape space had , and we compare that to the shape it now has , and thus we get a sense of " time ". further , we can create physical devices that change shape with a regularized velocity , and in a periodic way (" clocks " ) , and thus we can measure " time ". but there is not such a thing as " time " in and of itself. for example , space exists and a particular piece of space can be green. but there is no " green dimension " where green exists independently of space. green is a property of space. in a similar way , " time " is a property of space. " time " is the realization that space changes shape. but just as there is no " green dimension " so too is there no " time dimension " where time exists in and of itself. it makes sense to speak of a " time dimension " as a theoretical dimension. (i was standing in the kitchen , and now i'm at my desk. this change in the shape of space can be correctly plotted along a " time dimension " , but this plotting doesn't really exist in the real world ... it is simply a ( good , very good ) theoretical construct. ) what i mean by there is no " time dimension " is that there is no dimension called " time " out there in the real world that we can interact with in such ways as " time traveling ".

and this is how i ended up falling into studying relativity theory. after i realized this i remembered reading in stephen hawking's book , a brief history of time , something about time travel. i went back and flipped through the pages again , and , sure enough , he writes (to the effect ) that while he has seen no evidence of time travel it is theoretically possible (! ) ... he writes that it's totally possible that we have been visited by more technology advanced people from the future (! ) ... what ? ...

he believes that there is actually a dimension out there called " time " that can be traveled along ... !

for time travel to be possible that would mean that space would have to be making copies of itself every micro , micro second so that someone from the future has somewhere to come back to. for time travel to be possible , that means that the shape space had when i was stranding in the kitchen must be recorded somewhere , otherwise it would be impossible to travel back to it. for men from the future to travel back to right now (as stephen hawking's believes is possible ) that means that before this moment passes into the next and continues on for years and years to come , that space has to make copy of itself (of now , of this current shape ) so that they can come back here ! ... and there is no evidence that space is doing this

i was amazed to see stephen hawking seeing such a different world from me ... from my perspective he was totally wrong ... he hadn't really thought things through ... and this lead me to wonder how he got there , which (of course ) has to do with einstein's ideas (amongst other's ) and so i found myself wading through this poorly defined subject area called " relativity ".

while we use different terms (obviously you are educated in the area of physics ) , i believe that we might be in agreement (... yes ? )

where we might disagree is that i believe that time can expand or contract , however " before " and " after " are constants. that is , the changes in shape can speed up or slow down. and it seems (from what i've gleaned from einstein so far ) that einstein was rebelling against the idea that " the progression of time is constant " that there's some big pocket watch held by god that all things stay consistent with. so , i buy into his rebellion , but i don't seem to be buying to where he went with it. (again , i have to use the phrase " seem to " because i still don't understand what einstein means when he says " time " ... )

what is the definition of " time " ? ... is it " the regularized and periodic movement of a clock ? " ... is it " the recognition that the shape of space now is different that what it was before ? " ... or what ?

i've been reading through (trying hard , but not being very successful with it ) the Lorentz Transformation ... there's a variable in there called " time " ... but what is it ? ... i asked another guy this same question and he told me " time is one of the four dimensions in a euclidean mathematical model of space-time " ... oh brother ... is time the plotting of the changes of the shape of space ... so , t1 is me in the kitchen , t2 is me at my desk , and so on ... ?

another question i have for you is this ... did einstein say that if you travel faster than the speed of light , you travel backwards in time ? ... and , if so , do you have a reference for this ? (... a book reference would be great , ... and an u r l would be even better ! )

Reply (2)
One should realize that most words in everyday language are not unambiguously defined in terms of logic but have developed historically over thousands of years (you could in principle well do physics without even mentioning the words space and time just by giving a corresponding set of coordinates that determine the location of the object). Wittgenstein (in his Tractatus) notes that all problems in philosophy are in fact only due to a lack of proper definition within the language, a view that I would fully share (the well known 'chicken and egg' problem for instance is easily resolved if you refer the words uniquely to specific objects rather than to the generic idea of the words which can not be associated with a certain point in time).

Einstein determined time through identical and synchronized clocks, one in each of the two reference systems moving relatively to each other. However, he then inconsistently tried to reconcile the concept of relative motion with the invariance of the velocity of light, which he could only do by giving up his original definitions again and make space and time flexible. Let me demonstrate this at an example from mathematics:
If you have the two equations x=0 and x=1 then these are obviously contradictory. However, even some physicists try to 'solve' this 'system of equations' by adding up, as usual, the right and left hand sides which leads to 2x=1 or x=1/2. This is of course nonsense as the system is in mathematical terms over-determined and can therefore not be solved.
In a similar way does Relativity get its results and is thus obviously also flawed.

If you want to preserve your sanity then I wouldn't bother to read any Relativity books to get the definition of time because it isn't consistently given there. If not, any library should have something on the subject of Relativity, and usually also monographs etc. with reprints of Einstein's original papers (his paper 'On the Electrodynamics of Moving Bodies', in which his Special Relativity is developed, is in fact very banal and requires little or no knowledge of physics and it only appears difficult because of its conceptual inconsistencies).

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Any intellectual or scientific investigation of empirical phenomena is obviously limited by the methods and 'languages' we use and yields therefore basically only an 'operational' knowledge of the world. However, if the tools of investigation (i.e. the subjective components) are conceptually consistent and invariable, this enables therefore an objective rendering of the outer world, albeit only in this restricted sense.
If, like in Einstein's Relativity, the units of measure become variable as well, then there can obviously be no hope of being able to make any objective statements about the world at all and the theory becomes just a useless esoteric construction without any meaning.

In this sense, an observer- dependent (albeit constant) speed of light seems to be a flawed concept. However, although this severely restricts the consideration of a light signal as an independent physical object, it does not necessarily cause insurmountable logical problems if interpreted correctly (see the main Relativity Page).

The suggestion that gravitation defines an absolute reference frame for the propagation of light is interesting as it would seemingly explain the negative outcome of the Michelson- Morley Experiment (see the main page under Michelson- Morley Experiment) without the assumption of a constant speed of light.
It is however implausible that massless physical objects like electromagnetic waves should in any way be affected by gravitation at all (this argument holds of course for other suggested mechanisms like gravitational bending and redshift as well). More importantly, there is the logical problem that one couldn't define light propagation at points in space where the gravitational field is zero.
In any case, I am pretty sure that such an effect would have been detected already for instance when communicating with interplanetary spacecraft: the typical light travel time to the outer planets is a couple of hours and since most of the time is spent in interplanetary space (i.e. in the gravitational field of the sun) and the earth moves with about 30 km/sec with respect to the sun, this would lead to a deviation of about 1/10000 of the overall travel time, i.e. about 1 sec. This corresponds to a positioning error of 300000 km which I cannot imagine would have remained without significant problems for the close encounters with the planets (the typical maneuvering error in this case is a couple of minutes in spacecraft- flight time which translates into a position uncertainty of only a few thousand kilometers assuming a spacecraft velocity of around 20 km/sec ).

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I would certainly fully agree with your definition which more or less supports what I have been saying on these pages. However, on its own such general arguments are unlikely to convince physicists who tend to insist on the mathematical consistency of Einstein's Theory of Relativity including time dilation and length contraction. The point is that a 're-scaling' of the space and time units, albeit violating logical principles, seemed mathematically the only possible way for Einstein to account for the constancy of the speed of light, whereas he should have realized that it is the concept of 'speed' which has to be modified here (see my page regarding the Speed of Light and Theory of Relativity).

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The constancy of c in different reference frames can neither be proved through Maxwell' s Equations nor by the Michelson and Morley - Experiment:
the wave equation for the propagation of light (as derived from Maxwell's Equations) only yields an invariable speed because it is already implicitly assumed as constant in the definition for the magnetic field (in SI - units) or in the Lorentz- force (in Gaussian cgs- units). In fact, Maxwell himself would have expected a positive outcome of the Michelson and Morley- Experiment as he thought of electromagnetic waves as being attached to a hypothetical absolute reference frame (the 'ether'). As the expected result was not observed it was assumed that c could be taken as independent of the reference frame in Maxwell's Equations.

However as already explained on the main page, the outcome of the Michelson and Morley- Experiment is in principle only a logical consequence of an insufficient definition rather than of physical reality. The 'experiment' has only shown that light is not a disturbance of a 'medium' fixed relative to the sun, but this would be a rather trivial and useless insight.
The invariability of c can obviously only be proved by moving the source and receiver of the light signal relative to each other. Only this can justify using c as a unique quantity in Maxwell's Equations.

There is an unrelated logical problem with the Maxwell Equations if applied to a vacuum but this should not be relevant for the propagation of light waves.
Also, the Lorentz- Force is usually not unambiguously defined.

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As already mentioned on the main Relativity Page, the Lorentz- factor arises from the mistaken attempt to re-establish a vectorial velocity addition for light signals by re-scaling the space and time coordinates accordingly. The concept of a relativistic mass (or relativistic momentum) is therefore obviously also flawed and the alleged experimental evidence for the relativistic formula has to be explained by other physical phenomena or instrumental effects (if the observed 'relativistic' behaviour of charged particles in high energy accelerators for instance is indeed real, this would have to be interpreted as a velocity dependence of the electric and magnetic fields involved, i.e. E=E₀^.f(v/c) and B=B₀^.f(v/c) where f(v/c) is a suitable function of the velocity v of the particle relative to the object creating the electric or magnetic field).
Even if one wrongly assumed that mass would depend on velocity through the Lorentz factor, this would be dynamically irrelevant (i.e. unobservable) with the usual interpretation:
in the case of gravitational interaction it is reasonable to assume that gravitational and inertial mass are always strictly proportional (because both have obviously something to do with the same physical body) and therefore cancel out from the equation of motion (i.e. all bodies fall with the same acceleration in a given gravitational field);
for the electrostatic interaction, only the inertial mass appears in the equation of motion m*a = q*E, but the electric field E also would have to be scaled with the Lorentz factor because of length contraction, i.e. the acceleration would again be independent of the proposed relativistic mass increase.

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First of all: experiments can't prove something which is by definition logically impossible (if someone would claim his experiment proves that 0=1 to within 1 part in a billion, then there would be no need to even look at the evidence).
As already indicated both in this forum and the main page, 'time' can only be defined in terms of clocks or other regular events in nature and one has therefore to look for an actual physical cause for the temporary slowdown of the moving clock in corresponding experiments.

In the case of the 'airplane-experiment' the slowdown of the atomic clock could for instance be explained by the Lorentz- Force in the earth's magnetic field B: for typical aircraft speeds, the potential energy change in an atom due to the Lorentz Force (W_L=r₀*e*B*v/c (in Gaussian cgs-units with r₀= Bohr Radius; e= elementary charge)) is about a factor 10^-7 smaller than the potential energy of a quantum mechanical oscillator (W₀=h*ν) of a typical atomic clock (ν=1 GHz (=10⁹ Hz)). As the corresponding atomic transitions are spin- rather than orbit related, this is a second order effect. i.e. the frequency shift depends on the square of the electric potential. This yields therefore a similar order of magnitude for the resulting frequency shift as the relative time dilation suggested by Relativity (i.e. about 10^-13) and also the same velocity dependence ~(v/c)² (if v small compared to c). For a better estimate of this effect one would have to solve the Schrödinger Equation for the disturbed potential however. Other possible causes of a clock slowdown could be due to mechanical (i.e. non-gravitational) accelerations and/or vibrations which should induce disturbances in the inner-atomic fields and therefore a corresponding frequency change (again a quantum mechanical calculation might be necessary to confirm this quantitatively).

By the way, as far as I am aware, by no means all experimental data show clear evidence for the existence of time dilation both in Special and General Relativity, and those that are usually cited in support of this effect often have substantial systematic and/or statistical uncertainties.
Unfortunately, this counter- evidence is mostly suppressed (habitually if not systematically) as it obviously does not fit into the official view. But, as indicated above, 'experimental evidence' is anyhow irrelevant for a matter of conceptual consistency.

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Your question is a good point as it addresses one of the inconsistencies of Special Relativity:

Basically, propulsion is an application of the law of momentum conservation (i.e. Newton's law of action and reaction): if you eject material from the rocket in one direction, the rest of the rocket will gain exactly the corresponding momentum (m*v) in the opposite direction (this is a necessary consequence of a closed system and holds under any circumstances if you ignore certain quantum mechanical processes).
As the momentum gain during a given infinitesimal time interval should be independent of the reference frame and the latter can be chosen to co-move with the rocket, it is obvious that there is no limit to the velocity- and energy gain that can be achieved (neglecting friction effects and provided you don't run out of fuel of course).
As indicated on the main page of this site, it is however possible that electric and magnetic forces decrease as the velocity of the interacting particles becomes comparable to the speed of light. This could limit the exhaust velocity to values less than c and therewith the power of the rocket but not the rocket speed that can be achieved (any acceleration will eventually result in speeds higher than c if you just wait long enough (again neglecting friction)). In any case, mass (like charge) is a conserved quantity in mechanics and therefore does not depend on the velocity (the assumption of a velocity dependent mass results from the invalid procedure of re-scaling the space and time coordinates (see the main Relativity Page).

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You are right to assume that the examples you mention (cars on the road, light flashes) both lead to a change of the frequency (i.e. a Doppler effect), but your conclusion that this is a direct consequence of the velocity involved is incorrect (in the following I assume that the observer is at rest and the source moving instead; as velocities are only relative, this is equivalent but I find it somewhat easier to discuss):

If you imagine cars setting off from a car park at fixed time intervals (lets say 1 minute) and constant speed, then for a stationary observer down the road these cars will pass at exactly the same interval whatever the velocity of the cars (the only effect of a velocity increase would be a greater distance between the cars).
Now imagine that the cars are not setting off from a car park but (at the same rate) from a car transporter which is moving towards the observer but stops briefly each time a car is setting off. Obviously, the cars have here the same velocity on the road as before, but for the observer they would pass at a shorter time interval than 1 minute because the distance between the car transporter and the observer becomes progressively smaller .
Releasing the cars from the moving transporter would not make any difference for their frequency on the road but only for their spatial separation.

The above example is exactly analogous to the light flashes from a moving light source: one observes a higher flash rate compared to a stationary source because the flashes are released from a progressively decreasing distance to the observer but not because of the velocity as such (again, you could briefly stop the source moving while the flash is emitted and the observer would still see the higher flash rate).
The difference to the car example is that the velocity of the source during the emission of the flashes does not have an effect on the spatial distance of the signals (although this is of course again indirectly affected by the velocity due to the varying distance between source and observer). (note added later: strictly speaking one should actually not imagine the light flashes to have a spatial distance because this leads to contradictions regards the invariance of c in different reference frames (see lightspeed.htm)).
In other words, it is not an increase of the speed of light c which makes the time interval t=s/c smaller but a corresponding decrease of the distance s.

M.P.(2)
What I was referring to was the existence of the doppler effect caused by 'the observers motion', your reply referred to the doppler caused by the 'motion of the source'. The paradox I referred to applies only to the motion of the source in that you can not have a doppler effect caused by an observers motion and at the same time say that light speed relative to an observer remains c.

Reply(2)
As mentioned in my previous response, it does not make any difference if you assume the source resting and the observer moving or vice versa: the observed time-interval between the flashes depends only on the distance between the two at the moment the flash is emitted . As one is interested in the observed rather than the emitted flash-rate however, it is natural to put yourself into the observer's frame, i.e. assume the source as moving. This makes it more straightforward to calculate the travel time of the signal; if you put yourself into the position of the source, you would have the observer moving as well as the signal travelling and you would have to apply the principle of the constancy of c explicitly (i.e. the travel-time of the signal is independent of the movement of the observer and depends only on the distance between the two at the moment each flash is emitted).

As indicated earlier, the Doppler- shift is not due to the movement whilst the signal is emitted or detected but is a consequence of the changing distance the signal has to travel. Both for the car- and light-flash example you could stop the source or observer briefly whilst the flash is emitted or received and you would still see the Doppler shift (which is only caused by the changed distance between the two). The special situation with the propagation of light is however that only the separation at the moment of emission determines the travel time of the signal and any subsequent change of distance or velocity between source and observer is therefore without consequence for the Doppler -effect as well (this is the essence of the constancy of the speed of light).