Paradoxes of special relativity

Science and Technology
1

Are there any physicists (or other relativists) who will tackle some relativity paradoxes?

We are told that according to special relativity, SR, anything moving at the speed of light should have a zero time rate and zero length in the direction of relative motion. This is because of the Lorentz factor which is infinite at the speed of light. So it seems light should have no observed frequency or wavelength!

If instead the factor of infinity is applied to the measured properties of light then in its own reference frame it would have infinite frequency and wavelength. But an infinite wavelength implies a frequency of zero not infinity (the product of frequency and wavelength being the constant c).

It seems obvious that light behaves quite differently to matter and SR does not apply to light. Yet photons are said to have zero rest mass. They only have mass and energy because their zero rest mass is multiplied by infinity using SR. Hence if SR doesn’t apply to light it would have no mass, energy, frequency or even existence. So does SR apply to light or not?

2

How about the next paradox which is probably simpler. It only occurred to me 3 or 4 days ago so it may contain a loophole.

Imagine a light shining from a 1 metre long channel that is recessed below a flat surface. An opaque panel 1 metre long slides slowly along the surface and over the recess. As it does so, the light escaping from the recess reduces to zero for an instant. It then increases as the panel moves away from the recess.

According to SR if the panel moves fast enough its length would contract to half a metre. Light would then continue to leave the 1 metre long recess because no more than half of it would ever be covered by the contracted panel.

The same result is supposed to occur if the panel is at rest and the recessed light moves at (the same) high speed. The recess is now predicted to be half the length of the panel. So light does not emerge from the half metre long recess when it is covered by the one metre long panel.

How can the two different predictions produce the same result?

 

3

The next paradox targets Einstein’s attempt to apply the principle of frame equivalence to electrodynamics:

Imagine two small bodies are at the same horizontal level in a vacuum. They both have a mass of m and have equal electrical charges. The latter results in an electrostatic repulsion between the bodies of E. If the bodies fall downwards at a velocity of v there will be also be a magnetic attraction between them. This can be expressed as vM as the magnetic force varies with v. The net repulsion is then F = E - vM. So the instantaneous horizontal acceleration, as seen by an observer at rest, equals (E - vM)/γm. As usual γ (gamma) is 1/√(1 - v2/c2) and c is the speed of light. γ reflects special relativity’s prediction about the effect of a mass that moves in relation to an observer.

For an observer who also moves down at a velocity of v the two bodies are at rest, so there is no magnetic force and the acceleration is just E/m. If the moving and stationary observers are to measure the same acceleration then ÎłE = E - vM (after multiplying the equations in bold by Îłm) but if v>0 the left side of the equation exceeds E and the right is less than E. So why is it claimed that special relativity produces the same electromagnetic effects for all inertial observers?

(Each observer is predicted to see the same time dilation of the other observer’s frame. This symmetrical effect can’t remove the asymmetry in the horizontal accelerations (nor can the non-linearity of γ offset v). The electric charge is also the same for both observers.)

4

This next paradox seems fairly simple:

Suppose a rocket flies at high speed toward a stationary laser and carries equipment to measure the frequency of the laser’s light. The speed of the rocket is accurately known so the non-relativistic Doppler shift can be calculated. After allowing for this shift the measured frequency of the light should be slightly blueshifted. This is because the time rate of the atoms in the rocket will be slightly reduced due to its high speed, so in comparison the frequency of the laser’s atoms will be higher.

According to special relativity, the rocket can be regarded as being stationary whilst the laser moves at high speed. The time rate of the laser’s atoms is now reduced and this leads to a slight relativistic redshift being recorded by the “stationary” rocket.

When the data are analysed will they show a red or a blue shift? The recorded data surely do not change as the rocket decelerates. If the conflicting predictions cancel out then relativistic Doppler shifts do not occur. This is akin to the original clock paradox in which a clock cannot be both faster and slower than another.

The special theory of relativity requires equal time dilations to be observed from two frames in constant relative motion. The above contradiction shows why this has also been experimentally disproved. In practice unequal time dilations are observed.

5

Interesting points you bring up. I’d have to get the right synapses firing again to really get a grip on the stories. But I get the general idea

For me, the paradoxes indicate there is still something (some things) that we don’t know that could sort these out. It doesn’t necessarily mean that the Special Relativity is “wrong” - as I’ve seen some try to argue elsewhere.

 

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@mrmhead

Thanks for replying but the paradoxes show that SR’s predictions are contradictory and illogical. What more can be learnt about SR’s equation or about logic?

 

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I have more paradoxes but four should suffice. One disproof of a theory is sufficient.

Why has no one tried to use logic to defend SR? Are there no relativists who look at this Science and Technology forum?

Skeptics shouldn’t be emotionally wedded to a particular belief system, so they shouldn’t fear rational discussion.

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It seems obvious that light behaves quite differently to matter and SR does not apply to light. Yet photons are said to have zero rest mass. They only have mass and energy because their zero rest mass is multiplied by infinity using SR. Hence if SR doesn’t apply to light it would have no mass, energy, frequency or even existence. So does SR apply to light or not?
From what I understand the photons do not acquire physical mass from momentum, they acquire kinetic mass .

Imagine a 5000 lb car travelling @ 50mph. The car does not increase in physical mass, but when it smashes into a brick wall its momentum creates a kinetic force much greater than 5000lb . I am sure there is an equation that calculates this increase in force. Check out Inertia and Momentum.

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The impact force of the car equals the kinetic energy divided by the distance of the deceleration, but I’m talking about the mass of a photon not the force from a car. If a photon’s predicted zero rest mass cannot be multiplied by infinity then it has no mass or energy in a laboratory frame and hence cannot have a measurable frequency. Check out Planck’s equation.

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The impact force of the car equals the kinetic energy divided by the distance of the deceleration, but I’m talking about the mass of a photon not the force from a car. If a photon’s predicted zero rest mass cannot be multiplied by infinity then it has no mass or energy in a laboratory frame and hence cannot have a measurable frequency. Check out Planck’s equation.
Doesn't the double slit experiment prove that a photon exerts a massive force when it's wavefunction collapses against a solid object?

p.s. what’s the difference between momentum of a car and momentum of a photon?

p.p.s. I read this somewhere;

Photons have no REST mass, because they only exist travelling at the light velocity c. However, they do have a mass m (not a rest one !) given by the equation mc2 = h.nu, and their momentum is mc = h.nu/c as it should be.
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This isn’t what the double slit experiment proves. The momentum of anything comes from a moving mass, but if the moving mass is zero there is no momentum (unless perhaps if an infinite relative impact speed were possible).

If you take the time to study special relativity then we might have a worthwhile discussion, but I’m hoping to hear from someone who already understands the subject. Special relativity is a cornerstone of current physics so I think some of the contributors to this forum will already have studied it.

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@andrewsmith

Thanks for replying but the paradoxes show that SR’s predictions are contradictory and illogical. What more can be learnt about SR’s equation or about logic?
That's the point. We don't know what we don't know.

With these thought experiments, SR breaks down at the extremes - the paradoxes.

So maybe there is a new set of rules at the extremes. Just as Classical Mechanics works fine for most of what we can see, but taken to the extreme we need to switch to Quantum mechanics.

 

 

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SR is a theory specifically intended to work at extreme speeds. It a theory about light, so the fact that it is incompatible with light shows it is not fit for purpose.

The fourth paradox shows that at any non-zero speed a relativistic Doppler shift is predicted, but a contradictory shift is also predicted. This illogicality is an inevitable consequence of SR’s mistaken assumption that inertial frames must be equivalent. This assumption is clearly wrong. If one discards the medieval notion of relativity then all of the paradoxes can be avoided.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14
This isn’t what the double slit experiment proves. The momentum of anything comes from a moving mass, but if the moving mass is zero there is no momentum (unless perhaps if an infinite relative impact speed were possible).
Infinite relative speed ? What does that even mean?

The double slit experiment is an experiment that proves not only the wavelike behavior of an energetic particle, but also what gives it mass.

What you are proposing is that the equation E = Mc^2 is a contradiction, and AFAIK that proposition is just flat wrong.

Why does a moving photon E have the mass equal to Mc^2 ? Are you proposing that a moving photon does not have mass, because it does not travel @ “infinite relative speed”? I propose that a moving photon acquires mass because it travels @ finite speed, perhaps similar to an airplane breaking the sound barrier, which results in a sonic boom, a form of mass. Imagine two airplanes side by side, breaking the sound barrier. Would an interference pattern emerge as in the double slit experiment and produce a series of separated booms?

'The theory of relativity deduces, from its fundamental assumption, a clear and convincing answer to this question, an answer again of a quantitative character: all energy resists change of motion; all energy behaves like matter; a piece of iron weighs more when red-hot than when cool; radiation traveling through space and emitted from the sun contains energy and therefore has mass; the sun and all radiating stars lose mass by emitting radiation. This conclusion, quite general in character, is an important achievement of the theory of relativity and fits all facts upon which it has been tested". A. EINSTEIN AND L. INFELD, THE EVOLUTION OF PHYSICS, Page 208,
https://archive.org/stream/evolutionofphysi033254mbp/evolutionofphysi033254mbp_djvu.txt

So please explain the contradiction. I am really interested. Instead of drawing a lot of graphs with numbers and equations, can you provide a simple narrative, such as the one I quoted above?

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The fourth paradox shows that at any non-zero speed a relativistic Doppler shift is predicted, but a contradictory shift is also predicted. This illogicality is an inevitable consequence of SR’s mistaken assumption that inertial frames must be equivalent. This assumption is clearly wrong. If one discards the medieval notion of relativity then all of the paradoxes can be avoided.
Huh? Where does it say that inertial frames must be equivalent? Are you proposing that unequal frames of reference do not produce a Doppler effect at all?
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There is no point discussing this unless you understand Einstein’s theory. However SR’s predictions are based on quite simple equations so they are not very difficult to understand - apart from the fact that they are counter-intuitive. This makes it easy to get confused about which set of coordinates the various measurements refer to. Using commonsense makes matters worse, you need to stick to the equations. To get a fuller understanding of what Einstein had in mind you really need to read his 1905 paper rather than popular accounts of it.

The quote you gave about E=mc^2 is the usual propaganda. The relation between mass and energy has nothing to do with SR except in a cultural sense. Einstein wasn’t the first to use the equation, this seems to be in de Pretto’s 1903 paper (though the relation was derived by Poincare in 1900) and Einstein’s attempt to derive it in 1905 from SR failed. I haven’t tried to locate his later attempts but judging by the first attempt it seems to me that SR is incompatible with the equation, so I don’t know how a valid derivation would be possible. Again you need to study Einstein’s original paper on the subject (or in my case an English translation) rather than just popular accounts of it.

17
It seems obvious that light behaves quite differently to matter and SR does not apply to light. Yet photons are said to have zero rest mass. They only have mass and energy because their zero rest mass is multiplied by infinity using SR. Hence if SR doesn’t apply to light it would have no mass, energy, frequency or even existence. So does SR apply to light or not?

SR is a theory specifically intended to work at extreme speeds. It a theory about light, so the fact that it is incompatible with light shows it is not fit for purpose.


The photon has mass because it never accelerates and always has “constant velocity”. It is for all intent and purpose “at rest” and everything else is passing it @ “c”.

Therefore it is perfectly acceptable to say that the photon has rest mass, because it never accelerates or decelerates and is always at rest in its own relative frame of reference.

18

“The photon has mass because it never accelerates”. A photon is energy which is equivalent to mass. Have you ever wondered how this gets from the emitting particle to the absorbing one without accelerating to the speed of light and then decelerating again? A change of speed involves acceleration in the frame of a particle.

“Therefore it is perfectly acceptable to say that the photon has rest mass” - except physicists insist it has no rest mass, so it seems you are now trying to argue against SR rather than for it.

I addressed the paradoxes to physicists or to people who understand relativity. So this thread doesn’t apply to you. If you are interested in SR I suggest you learn what it means. In the meantime you could start your own thread about what you’d like SR to mean, but please don’t try to waste any more of my time.

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“Therefore it is perfectly acceptable to say that the photon has rest mass” – except physicists insist it has no rest mass, so it seems you are now trying to argue against SR rather than for it.
No, I am not arguing that photon have no zero rest mass if they would ever be at rest. I am arguing that the proposition of a photon ever being at rest is purely theoretical.Photons are never at rest and always in a state of constant velocity, i.e. "c" and therefore always have mass associated with being at relative rest.
I addressed the paradoxes to physicists or to people who understand relativity. So this thread doesn’t apply to you. If you are interested in SR I suggest you learn what it means. In the meantime you could start your own thread about what you’d like SR to mean, but please don’t try to waste any more of my time.
I understand quite well what SR means. I need not know the maths in order to understand the principles.

A photon does not accelerate. It attains “c” instantly. It is a quantum and subject to QM. The instant the photon is emitted it travels @ “c”.

It is never at rest as a photon and never needs accelerating! It can do that because it has no real rest mass that needs accelerating!!

I’ll leave that to you to find the maths, OK?